Using the Chain Rule with a Table
Using the chain rule to find derivates with some values given in a table
Using the Generalized Power Rule
Author: ShaNisaa RaSun
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Answer" to reveal the answer to the problem.
Problem: Find the derivative of the following function.\[y=3(2x+e^x)^5\]
\(\dfrac{dy}{dx}= 15(2x+e^x)^4(2+e^x)\)
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MLC WIR 20B M151 week6 #4a
Using logarithmic differentiation to find the derivative of a function
MLC WIR 20B M151 week6 #7
Finding the speed of an object given a vector function for its position
MLC WIR 20B M151 week6 #8
Finding the point when the tangent line to a function has a particular slope
MLC WIR 20B M151 week6 #12
Using the derivative to find the total distance traveled by a particle
MLC WIR 20B M151 week6 #13
Finding where the tangent line is horizontal or vertical for a parametric equation
MLC WIR 20B M151 week6 #14
Finding the equation of a tangent line to a parametric curve
MLC WIR 20B M151 week6 #15
Finding the equation of a tangent line to an implicit function
MLC WIR 20B M151 week6 #16
Solving for constants so that a piecewise function is differentiable everywhere
MLC WIR 20B M151 week6 #11
Using a linear approximation to approximate the value of a function
MLC WIR 20B M151 week7 #1a
Finding the absolute maximum and absolute minimum values of a function on a closed interval
MLC WIR 20B M151 week7 #2a
Finding a number that satisfies the conclusion of the Mean Value Theorem on an interval
MLC WIR 20B M151 week7 #2b
Finding a number that satisfies the conclusion of the Mean Value Theorem on an interval
MLC WIR 20B M151 week7 #3
Sketching a curve given information about the function and its derivatives
MLC WIR 20B M151 week7 #4a
Evaluating a limit using L'Hospital's Rule
MLC WIR 20B M151 week7 #5
Using the first and second derivatives to sketch the graph of a function
MLC WIR 20B M151 week8 #1
Solving a word problem minimizing area
MLC WIR 20B M151 week8 #2
Solving a word problem maximizing area
MLC WIR 20B M151 week8 #3
Finding the point on a line closest to a point
MLC WIR 20B M151 week8 #5b
Antidifferentiating twice to find a function from its second derivative
MLC WIR 20B M151 week8 #5c
Antidifferentiating twice to find a function from its second derivative
MLC WIR 20B M151 week8 #5d
Antidifferentiating to find a function from its derivative
MLC WIR 20B M151 week8 #5e
Antidifferentiating twice to find a function from its second derivative
MLC WIR 20B M151 week8 #5f
Antidifferentiating twice to find a function from its second derivative
MLC WIR 20B M151 week8 #6
Using antidifferentiation to find the height of a cliff from the impact speed of a dropped stone
MLC WIR 20B M151 week9 #10e
Antidifferentiating twice to find a function from its second d
MLC WIR 20B M151 week9 #10f
Antidifferentiating twice to find a function from its second d
MLC WIR 20B M151 week9 #10a
Finding the antiderivative of a polynomial
MLC WIR 20B M151 week9 #10b
Finding the antiderivative of a rational function
MLC WIR 20B M151 week9 #10c
Finding the antiderivative of a function with secant and tangent
MLC WIR 20B M151 week9 #8e
Evaluating a limit with an indeterminant product using L'Hospital's Rule
MLC WIR 20B M151 week9 #9
Finding a number that satisfies the conclusion of the Mean Value Theorem for a function on an interval
MLC WIR 20B M151 week9 #1
Determining the properties of a function from the graph of its derivative
MLC WIR 20B M151 week9 #2
Using the derivative to determine where a function is increasing and decreasing
MLC WIR 20B M151 week9 #3
Finding the absolute maximum and minimum values of a function on a closed interval
MLC WIR 20B M151 week9 #4
Finding the intervals where a function is increasing and decreasing and its local maximums and minimums
MLC WIR 20B M151 week9 #5
Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points
MLC WIR 20B M151 week9 #6
Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points
MLC WIR 20B M151 week9 #7
Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points
MLC WIR 20B M151 week10 #12
Finding the tangent line to a parametric curve
MLC WIR 20B M151 week10 #13
Finding when the tangent line to a parametric curve is vertical or horizontal
MLC WIR 20B M151 week10 #15
Determining the rate that the area of a triangle is increasing based on the rate an angle is increasing
MLC WIR 20B M151 week10 #16
Using a linear approximation to estimate the value of a function
MLC WIR 20B M151 week10 #17
Finding the value for a function that satisfies the Mean Value Theorem on an interval
MLC WIR 20B M151 week10 #18
Determining the properties of a function from the graph of its derivative
MLC WIR 20B M151 week10 #19a
Using L'Hospital's Rule to solve a limit
MLC WIR 20B M151 week10 #19b
Using L'Hospital's Rule to solve a limit with an indeterminant product
MLC WIR 20B M151 week10 #19c
Using L'Hospital's Rule to solve a limit with an indeterminant difference
MLC WIR 20B M151 week10 #6c
Using L'Hospital's Rule to evaluate a limit representing a derivative at a point
MLC WIR 20B M151 week10 #8c
Evaluating the limit at infinity of a fraction with exponential functions
MLC WIR 20B M151 week10 #8d
Evaluating the limit at negative infinity of a fraction with exponential functions
MLC WIR 20B M151 week10 #9a
Finding a derivative using the Product Rule
MLC WIR 20B M151 week10 #9d
Finding a derivative using the Quotient Rule
MLC WIR 20B M151 week10 #10a
Finding the derivative of an implicit function
MLC WIR 20B M151 week10 #24c
Evaluating a definite integral with an exponential and sine function
Review for the Common Exam: MATH 152 Exam 2 b Review Problems 8 & 9
Review of improper integrals and the Comparison Theorem
Review for the Common Exam: MATH 152 Exam 3 c Review Problems 13-18
Review of Taylor and Maclaurin Series and their properties
Review for the Common Exam: MATH 152 Exam 3 c Review Problems 19 & 20
Review of Taylor Polynomials and Taylor's Inequality
WIR 20B M152 V90
Finding the surface area of a rotated parametric curve
WIR 20B M152 V96
Finding the area of a region defined using polar coordinates
WIR 20B M152 V82
Finding the Taylor series of a function
Taylor and Maclaurin Series: MATH 152 11.10 Problems 4-10
Finding Taylor and Maclaurin Series for functions
WIR 20B M152 V76
Finding a power series representation for a function
WIR 20B M152 V10
Finding the area of a region bounded by curves
MATH 152: Integration by Parts Exercise 1
Solving an indefinite integral with an exponential function using integration by parts
MATH 152: Integration by Parts Exercise 2
Solving a definite integral with an exponential function using integration by parts
MATH 152: Integration by Parts Exercise 8
Solving an indefinite integral with an exponential function using integration by parts
MATH 152: Integration by Parts Exercise 9
Using integration by parts twice for an integral with sine and an exponential function
WIR 20B M152 V22
Evaluating an integral using integration by parts
WIR 20B M152 V26
Evaluating an integral using integration by parts
MATH 152: u-Substitution Exercise 6
Using u-substitution on an indefinite integral with an exponential function, sine, and cosine
MATH 152: u-Substitution Exercise 8
Using u-substitution to solve an indefinite integral with an exponential function
WIR 20B M152 V1
Integrating an exponential function using u-substitution
WIR 20B M152 V43
Using the comparison test to determine if an improper integral converges or diverges
Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3
Proving facts about the derivatives of vector functions including the product rule
Derivatives and Applications: MATH 171 Problems 7 & 8
Calculating slopes of tangent lines to parametric curves
Derivatives and Applications: MATH 151 K.2 Problems 9-15
Tangent lines to parametric equations and related rates examples
Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29
Related rates problems, differentials, linear and quadratic approximations
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for Common Exam: MATH 151 Exam 3 Review Problems 22-24
Optimization problems
Inverse Trigonometric Functions: MATH 171 Problems 4-6
Properties of inverse trig functions and the derivative of arctangent
Inverse Trigonometric Functions: MATH 151 1.5 Problems 9-12
Properties and derivatives of inverse trigonometric functions
Derivatives and Rates of Change: MATH 171 Problems 1-3
Using the limit definition to find derivatives of functions and vector functions
Differentiation Formulas: MATH 171 Problems 4 & 5
Using the limit definition to find a derivative and proving the power rule
Differentiation Formulas: MATH 171 Problems 6 & 7
Proving the Product Rule and the rule for the derivative of a difference of functions
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Differentials: MATH 171 Problems 1 & 2
Proving facts about differentials including a product rule
Differentials and Approximations: MATH 151 3.10 Problems 1-6
Differentials, linear approximations and quadratic approximations
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 1-3
Proving the derivatives of trigonometric functions and that sine is continuous
Implicit Differentiation: MATH 171 Problems 6 & 7
Using implicit differentiation to solve a problem and to prove the power rule for rational exponents
Implicit Differentiation: MATH 151 3.5 Problems 10-13
Implicit differentiation and finding tangent lines
Inverse Trigonometric Functions: MATH 151 Problems 9-12
Properties and derivatives of inverse trigonometric functions
Derivatives and Applications: MATH 151 3.9 Problems 9-15
Tangent lines to parametric equations and related rates examples
Studying the Shape of Curves: MATH 151 4.1 Problems 2-7
Using derivatives to find properties of graphs
Absolute Extrema: MATH 171 Problems 4 & 5
Proving Fermat's Theorem and graphing local and absolute extrema
Mean Value Theorem: MATH 171 Problems 6-8
Using the Mean Value Theorem to prove facts about functions
Studying the Shape of Curves: MATH 171 Problems 1-3
What the derivatives of a function tell us about the shape of its graph
Studying the Shape of Curves: MATH 151 Problems 2-7
Using derivatives to find properties of graphs
L'Hospital's Rule: MATH 151 4.4 Problem 1(a-h)
Using L'Hospital's Rule to solve limits
Optimization: MATH 171 Problems 1-3
Optimizing values in word problems
Antiderivatives: MATH 171 Problems 4-6
Proving facts about antiderivatives and a physics application
Fundamental Theorem of Calculus: MATH 171 Problems 1-3
Proving and then applying the Fundamental Theorem of Calculus
Integration by Substitution: MATH 151 5.5 Problems 13 & 14
Examples of integration by substitution
Review for the Common Exam: MATH 152 Exam 2 b Review Problems 8 & 9
Review of improper integrals and the Comparison Theorem
Review for the Common Exam: MATH 152 Exam 3 c Review Problems 13-18
Review of Taylor and Maclaurin Series and their properties
Review for the Common Exam: MATH 152 Exam 3 c Review Problems 19 & 20
Review of Taylor Polynomials and Taylor's Inequality
Increasing, Decreasing, and Non Monotonic Sequences
Explaining increasing, decreasing, and non monotonic for sequences
Taylor and Maclaurin Series: MATH 152 11.10 Problems 4-10
Finding Taylor and Maclaurin Series for functions
Integration by Parts: MATH 172 Problems 1 & 2
Proving the formula for integration by parts and a reduction formula
WIR2 20B M251 V7
Finding the limit of a three-dimensional vector function
WIR2 20B M251 V8
Finding a vector equation for the tangent line to a three-dimensional vector function
WIR2 20B M251 V9
Finding the angle of intersection for two three-dimensional vector functions
WIR2 20B M251 V10
Finding the length of a three-dimensional curve
WIR2 20B M251 V11
Finding the curvature of a three-dimensional vector function
WIR3 20B M251 V8
Finding the partial derivatives of a function of two variables
WIR3 20B M251 V11
Finding all second-order partial derivatives of a function of two variables
WIR4 20B M251 V9
Finding the absolute maximum and minimum values of a function of two variables on a rectangle
WIR4 20B M251 V10
Finding the absolute maximum and minimum values of a function of two variables on a triangular region
WIR5 20B M251 V7
Evaluating a double integral over a given region
WIR5 20B M251 V10
Evaluating a double integral by reversing the order of integration
WIR8 20B M251 V1
Evaluating a line integral along half a circle
WIR8 20B M251 V2
Evaluating a line integral along a curve in space
WIR8 20B M251 V3
Evaluating a line integral along a curve
WIR8 20B M251 V6
Evaluating a line integral of a vector field along an curve
WIR8 20B M251 V7
Evaluating a line integral of a vector field along a curve in space
WIR8 20B M251 V8
Using a line integral to find the work done by a force field moving a particle along a curve
WIR9 20B M251 V5
Finding the curl and divergence of a three dimensional vector field
WIR10 20B M251 V4
Evaluating a surface integral of a vector field
MATH 308 WIR22A V15
Solving an initial value problem including air resistance for the path of a thrown ball to determine the maximum height it reaches
Matrix Derivative and Integral
Explaining how to find the derivative and integral of matrix and vector functions
Scalar-Valued IVP
Showing how the exponential function is the solution to an initial value problem
MATH 152: Sequences Exercise 4
Finding the limit of a sequence
MATH 152: Sequences Exercise 6
Finding the limit of a sequence using logarithm properties
MATH 152: Sequences Exercise 7
Finding the limit of a sequence
Increasing, Decreasing, and Non Monotonic Sequences
Explaining increasing, decreasing, and non monotonic for sequences
MATH 152: Sequences Exercise 10
Determining if a sequence is increasing, decreasing, or non monotonic
WIR 20B M152 V45
Determining if a sequence converges or diverges
The Chain Rule (multivariable) Conceptual V1
Explaining the Chain Rule for multivariable functions
The Chain Rule (multivariable) Exercise V3
Using the Chain Rule for multivariable functions to find the rate a volume is changing
Finding the nth Taylor Polynomial Exercise
Finding the nth Taylor polynomial of the natural log function centered at 1
Approximation Using Taylor Polynomials Exercise
Using a Taylor polynomial to approximate the value of a function and estimating the error
The Chain Rule (multivariable) Conceptual V1
Explaining the Chain Rule for multivariable functions
Math 140 5.4 Exercise 3
Rewriting a function with a fractional exponent in radical form
WIR4 20B M150 V21
Solving an equation with logarithmic functions
WIR4 20B M150 V22
Solving an equation with logarithmic functions
WIR4 20B M150 V23
Solving an equation with logarithmic functions
WIR4 20B M150 V24
Solving an equation with logarithmic functions
WIR8 20B M150 V11
Solving an equation with logarithmic functions
Math 140 Exam 3 Review Exercise 21
Solving equations with exponentials and logarithms
Math 140 Exam 3 Review Exercise 23
Solving equations with exponentials and logarithms
Math 140 Exam 3 Review Exercise 13
Stating the domain in interval notation of a function with radicals, fractions, and exponentials
Math 140 Exam 3 Review Exercise 17
Calculating continuously compounded interest for money in an account
Math 140 Exam 3 Review Exercise 19
Writing logarithmic equations in exponential form
Math 140 Exam 3 Review Exercise 20
Solving equations with exponentials and logarithms
Composition of Logarithmic and Exponential Functions
Finding the composition of two functions with exponentials and logarithms
An Equation with an Exponential Function
Solving a equation with an exponential function
An Equation with Exponential Functions of Different Bases
Solving an equation with two exponential functions with different bases
Factoring a Quadratic-Like Equation with Exponentials
Solving an equation with exponential functions by factoring
Factoring an Equation with Exponentials
Solving a equation with exponential functions by factoring
Population Model with Exponential Growth
Finding the size of a population of rabbits with exponential growth
Population Model with Exponential Decay
Finding the size of a population of rabbits with exponential decay
Horizontal Asymptote of an Exponential Function
Finding the horizontal asymptote of an exponential function
Horizontal Asymptote of an Exponential Function (2)
Finding the horizontal asymptote of an exponential function
Horizontal Asymptote of an Exponential Function (3)
Finding the horizontal asymptote of an exponential function
A Composition of Tangent and Arccosine
Evaluating a composition of tangent and arccosine
WIR 20B M152 V51
Determining if a series converges or diverges
WIR 20B M152 V53
Determining if a series converges or diverges and find the sum if it converges
WIR 20B M152 V58
Using the comparison test to determine if a series converges or diverges
WIR 20B M152 V59
Using the limit comparison test to determine if a series converges or diverges
WIR 20B M152 V63
Using the Alternating Series Test to determine if a series converges or diverges
Numerical Calculations in Python
Performing basic numerical calculations in Python
Parametric Plots and Tangents at a Given t-value in Python
Using Python to find the tangent line to a parametric equation and plot the two graphs
Tangents to Parametrized Curves at a Given Point in Python
Using Python to plot a parametrized curve and its tangent line at a point
Approximating Definite Integrals with Riemann Sums in Python
Using Python to approximate a definite integral using left endpoint Riemann sums
Finding and Graphing Tangent Lines to a Curve in Python
Using Python to find the equation of the tangent line to a curve and graphing the result
Finding Derivatives in Python
Finding derivatives in Python and solving for the rate of change of a force
Finding Horizontal Tangent Lines in Python
Finding when the tangent line to a function is horizontal in Python
Finding Intervals of Increase/Decrease and Concavity in Python
Using Python to find the intervals where a function is increasing or decreasing
List Comprehension and Patterns in Higher Derivatives in Python
Using Python's list comprehension tool to find several higher order derivatives of a function at once
Domain of Combinations of Functions Video 4
Finding the domain of a function with a root and a logarithm in the denominator
Properties of Radical Functions and Expressions Video 2
How to rewrite radical terms as power terms
Properties of Power and Exponential Expressions Video 6
Simplifying power and exponential expressions using properties of exponents
Properties of Power and Exponential Expressions Video 7
Simplifying power and exponential expressions using properties of exponents
Properties of Power and Exponential Expressions Video 9
Simplifying an expression with both power and exponential functions using properties of exponents
Properties of Power and Exponential Expressions Video 1
Properties of exponents applied to power and exponential expressions
Properties of Power and Exponential Expressions Video 2
Properties of multiplying and simplifying power and exponential expressions
Properties of Power and Exponential Expressions Video 3
Properties of exponents applied to power and exponential expressions
Properties of Power and Exponential Expressions Video 4
Properties of exponential growth and decay functions
Properties of Power and Exponential Expressions Video 5
Properties of the exponential function with base e
Solving Power and Exponential Equations Video 1
Explaining how to solve equations with power and exponential terms
Solving Power and Exponential Equations Video 2
Solving equations with exponential terms
Solving Power and Exponential Equations Video 3
Solving equations with base e exponential terms
Properties of Logarithmic Functions and Expressions Video 1
Explaining the terminology and rules of logarithms
Solving Logarithmic Equations Video 1
Explaining how to solve logarithmic equations
Solving Logarithmic Equations Video 2
Solving logarithmic equations with a single logarithm term
Solving Logarithmic Equations Video 3
Solving logarithmic equations with multiple logarithm terms
Solving Logarithmic Equations Video 4
Solving logarithmic equations with multiple logarithm terms on both sides
Properties of Power and Exponential Expressions Video 1
Properties of exponents applied to power and exponential expressions
Properties of Power and Exponential Expressions Video 2
Properties of multiplying and simplifying power and exponential expressions
Properties of Power and Exponential Expressions Video 3
Properties of exponents applied to power and exponential expressions
Properties of Power and Exponential Expressions Video 4
Properties of exponential growth and decay functions
Properties of Power and Exponential Expressions Video 5
Properties of the exponential function with base e
Properties of Logarithmic Functions and Expressions Video 1
Explaining the terminology and rules of logarithms
Introduction to Riemann Sums
Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative