Using the Chain Rule with a Table
Using the chain rule to find derivates with some values given in a table
Using the Generalized Exponential 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 \(\dfrac{dy}{dx}\) of the following function.\[y=14^{e^x+\log_4(x)+4x^8}\]
\(\dfrac{dy}{dx}= 14^{e^x+\log_4(x)+4x^8}(\ln(14)) \left(e^x+\dfrac{1}{x\ln(4)}+32x^7\right)\)
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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 #19d
Using L'Hospital's Rule to solve a limit with an indeterminant power
MLC WIR 20B M151 week10 #23a
Evaluating an indefinite integral by simplifying a fraction to powers of x
MLC WIR 20B M151 week10 #24b
Evaluating a definite integral by first simplifying the integrand
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 #8e
Evaluating a limit at infinity by combining logarithms
MLC WIR 20B M151 week10 #24e
Using u-substitution to evaluate an indefinite integral
MLC WIR 20B M151 week10 #9d
Finding a derivative using the Quotient Rule
MLC WIR 20B M151 week10 #10b
Finding the derivative of an implicit function
Review for the Common Exam: MATH 152 Exam 3 b Review Problem 6
Review of estimating the sum of a series and the remainder
Review for the Common Exam: MATH 152 Exam 3 b Review Problems 4 & 5
Review of using tests to determine if a series is absolutely convergent, convergent, and divergent
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 10-13
Review of power series properties and writing functions as power series
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
Review for the Common Exam: MATH 152 Exam 3 c Review Problems 4 & 5
Review of using tests to determine if a series is absolutely convergent, convergent, and divergent
WIR 20B M152 V88
Finding the length of a curve given by parametric equations
WIR 20B M152 V96
Finding the area of a region defined using polar coordinates
Taylor and Maclaurin Series: MATH 152 11.10 Problems 4-10
Finding Taylor and Maclaurin Series for functions
WIR 20B M152 V81
Finding the Taylor series of a function
WIR 20B M152 V69
Determining if a series is absolutely convergent, conditionally convergent, or divergent.
WIR 20B M152 V70
Determining if a series is absolutely convergent, conditionally convergent, or divergent.
WIR 20B M152 V75
Finding the interval and radius of convergence for a power series
WIR 20B M152 V77
Finding a power series representation for a function
Representations of Functions as Power Series: MATH 152 11.9 Problems 2 & 3
Finding power series representations for functions and the radius and interval of convergence of the power series
WIR 20B M152 V10
Finding the area of a region bounded by curves
WIR 20B M152 V15
Finding the volume of a solid of revolution using the washer method
WIR 20B M152 V17
Finding the volume of a solid of revolution using cylindrical shells
WIR 20B M152 V22
Evaluating an integral using integration by parts
WIR 20B M152 V23
Evaluating an integral using integration by parts
WIR 20B M152 V26
Evaluating an integral using integration by parts
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 4
Solving an indefinite integral with a natural logarithm using integration by parts
MATH 152: Integration by Parts Exercise 5
Solving a definite integral with a natural logarithm 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 V1
Integrating an exponential function using u-substitution
WIR 20B M152 V2
Integrating a rational function using u-substitution
WIR 20B M152 V3
Integrating a rational function using u-substitution
MATH 152: u-Substitution Exercise 4
Using u-substitution to evaluate a definite integral with a natural logarithm
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 V34
Evaluating an integral using integration by parts
WIR 20B M152 V35
Evaluating an integral using integration by parts
WIR 20B M152 V35.5
Evaluating an integral using integration by parts
WIR 20B M152 V43
Using the comparison test to determine if an improper integral converges or diverges
MATH 152: Improper Integrals Exercise 2
Solving an improper integral where the upper limit of integration is infinity
MATH 152: Improper Integrals Exercise 4
Solving an improper integral where the upper limit of integration is infinity
MATH 152: Improper Integrals Exercise 6
Solving an improper integral where the upper limit of integration is infinity
Vectors and Derivatives: MATH 151 K.1 Problems 1-8
Derivatives and vectors with some physics applications
Review for the Common Exam: MATH 151 Exam 2 Review Problems 10-15
Implicit differentiation and physics applications of derivatives
Review for the Common Exam: MATH 151 Exam 2 Review Problems 16-20
Derivatives of parametric equations and tangent lines
Review for the Common Exam: MATH 151 Exam 2 Review Problems 1-9
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30
Antiderivatives and physics applications
Higher Order Derivatives: MATH 171 Problems 4-6
Finding a formula for a higher order derivative and a formula for the second derivative of a product
Trigonometry Derivatives and the Chain Rule: MATH 151 3.3 Problems 1-9
Derivatives of trigonometric functions and using the Chain Rule
Trigonometry Derivatives and the Chain Rule: MATH 151 3.4 Problems 1-9
Derivatives of trigonometric functions and using the Chain Rule
Vectors and Derivatives: MATH 151 3.4 Problems 1-8
Derivatives and vectors with some physics applications
Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 4 & 5
Using the Chain Rule to prove facts about derivatives
Studying the Shape of Curves: MATH 151 4.1 Problems 2-7
Using derivatives to find properties of graphs
Studying the Shape of Curves: MATH 151 Problems 2-7
Using derivatives to find properties of graphs
Integration by Substitution: MATH 171 Problems 4-6
Using u substitution to evaluate integrals and prove facts about logarithms and integrals and
Review for the Common Exam: MATH 152 Exam 3 b Review Problem 6
Review of estimating the sum of a series and the remainder
Review for the Common Exam: MATH 152 Exam 3 b Review Problems 4 & 5
Review of using tests to determine if a series is absolutely convergent, convergent, and divergent
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 10-13
Review of power series properties and writing functions as power series
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
Review for the Common Exam: MATH 152 Exam 3 c Review Problems 4 & 5
Review of using tests to determine if a series is absolutely convergent, convergent, and divergent
Taylor and Maclaurin Series: MATH 152 11.10 Problems 4-10
Finding Taylor and Maclaurin Series for functions
Representations of Functions as Power Series: MATH 152 11.9 Problems 2 & 3
Finding power series representations for functions and the radius and interval of convergence of the power series
Integration Using Partial Fractions: MATH 172 Problems 8 & 9
Finding a partial fraction decomposition and integrating using partial fractions
WIR2 20B M251 V6
Determining the domain of a three-dimensional vector function
WIR2 20B M251 V7
Finding the limit of a three-dimensional vector function
WIR2 20B M251 V12
Finding the position vector function given the velocity and an initial position
WIR3 20B M251 V1
Finding and sketching the domain of a function of two variables
WIR3 20B M251 V11
Finding all second-order partial derivatives of a function of two variables
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 V4
Evaluating a line integral along a curve
WIR8 20B M251 V5
Evaluating a line integral along a curve in space
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
Scalar-Valued IVP
Showing how the exponential function is the solution to an initial value problem
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
WIR 20B M152 V45
Determining if a sequence converges or diverges
WIR 20B M152 V48
Determining if a sequence is increasing, decreasing, or not monotonic and if it is bounded
Finding the nth Taylor Polynomial Exercise
Finding the nth Taylor polynomial of the natural log function centered at 1
Math 140 5.4 Exercise 3
Rewriting a function with a fractional exponent in radical form
Math 140 Exam 3 Review Exercise 24
Find the domain of a function in interval notation with a fraction and logarithm
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 18
Using properties of logarithms to write an expression as a single logarithm
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
Expanding a Logarithmic Expression
Expanding a logarithmic expression using logarithm properties
Condensing a Logarithmic Expression
Condensing logarithmic expressions into a single logarithm
Evaluating Logarithmic Expressions
Finding the exact value of logarithms using logarithmic properties
Vertical Asymptote of a Logarithmic Function
Finding the vertical asymptote of a logarithmic function
Vertical Asymptote of a Logarithmic Function (2)
Finding the vertical asymptote of a logarithmic function
Domain and x-intercepts of a Logarithmic Function
Finding the domain and x-intercepts of a logarithmic function
Domain and x-intercepts of a Logarithmic Function (2)
Finding the domain and x-intercepts of a logarithmic function
Solving an Equation with Logarithms
Solving a logarithmic equation using properties of logarithms
Solving an Equation with a Logarithmic Function
Solving a logarithmic equation using properties of logarithms
A Composition of Tangent and Arccosine
Evaluating a composition of tangent and arccosine
WIR 20B M152 V53
Determining if a series converges or diverges and find the sum if it converges
WIR 20B M152 V56
Using the comparison test to determine if a series converges or diverges
WIR 20B M152 V57
Using the comparison test to determine if a series converges or diverges
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
Approximating Definite Integrals with Riemann Sums in Python
Using Python to approximate a definite integral using left endpoint Riemann sums
Domain Restrictions
Explaining domain restrictions for denominators, even roots, and logarithms
Domain of Logarithmic Functions Video 1
Finding the domain of a logarithmic function
Domain of Combinations of Functions Video 1
Finding the domain of a function with a denominator, square root, and logarithm
Domain of Combinations of Functions Video 2
Finding the domain of a function with a natural logarithm and 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
Properties of Logarithmic Functions and Expressions Video 2
Explaining the basic properties of logarithmic functions
Properties of Logarithmic Functions and Expressions Video 3
Expanding logarithmic expressions using logarithm rules
Properties of Logarithmic Functions and Expressions Video 4
Condensing a logarithmic expression into a single logarithm
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 2
Explaining the basic properties of logarithmic functions
Introduction to Riemann Sums
Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums