VMLC
Release-50
Tags:DerivativeExponential FunctionChain RuleHow-To CalculusGeneralized Power Rule

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.

Exercises

\(\dfrac{dy}{dx}= 15(2x+e^x)^4(2+e^x)\)

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Evaluating a Definite Integral 2 thumbnail
Using the Fundamental Theorem of Calculus to evaluate a definite integral

Evaluating a Definite Integral with u-Substitution

Evaluating a Definite Integral with u-Substitution thumbnail
Using the Fundamental Theorem of Calculus and \(u\)-substitution to evaluate a definite integral

Evaluating a Limit Numerically

Evaluating a Limit Numerically thumbnail
Finding the limit of a function numerically using a calculator

Evaluating Limits Algebraically

Evaluating Limits Algebraically thumbnail
Using the properties of limits to find several limits algebraically

Evaluating Limits from a Graph

Evaluating Limits from a Graph thumbnail
Finding limits from the graph of a piecewise function

Evaluating One-Sided Limits from a Graph

Evaluating One-Sided Limits from a Graph thumbnail
Finding one-sided limits from the graph of a piecewise function

Exponential Growth and Decay in Discrete Time

Exponential Growth and Decay in Discrete Time thumbnail
Explaining exponential functions in discrete time

Exponential Growth in Discrete Time Example

Exponential Growth in Discrete Time Example thumbnail
Solving a population example of exponential growth in discrete time

Factoring a Quadratic-Like Equation with Exponentials

Factoring a Quadratic-Like Equation with Exponentials thumbnail
Solving an equation with exponential functions by factoring

Factoring an Equation with Exponentials

Factoring an Equation with Exponentials thumbnail
Solving a equation with exponential functions by factoring

Finding an Antiderivative

Finding an Antiderivative thumbnail
Finding the antiderivative of a function

Finding and Graphing Tangent Lines to a Curve in Python

Finding and Graphing Tangent Lines to a Curve in Python thumbnail
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 thumbnail
Finding derivatives in Python and solving for the rate of change of a force

Finding Horizontal Tangent Lines in Python

Finding Horizontal Tangent Lines in Python thumbnail
Finding when the tangent line to a function is horizontal in Python

Finding Intervals of Increase/Decrease and Concavity in Python

Finding Intervals of Increase/Decrease and Concavity in Python thumbnail
Using Python to find the intervals where a function is increasing or decreasing

Finding Marginal Cost and Marginal Average Cost

Finding Marginal Cost and Marginal Average Cost thumbnail
Finding the derivative of both the cost function and average cost function

Finding the Cost Function from Marginal Cost

Finding the Cost Function from Marginal Cost thumbnail
Solving the antiderivative of marginal cost to find the cost function and evaluating a particular cost

Finding the Derivative of a Polynomial Using the Limit Definition

Finding the Derivative of a Polynomial Using the Limit Definition thumbnail
Using the limit definition to find the derivative of a polynomial

Finding the Derivative of a Rational Function Using the Limit Definition

Finding the Derivative of a Rational Function Using the Limit Definition thumbnail
Using the limit definition to find the derivative of a rational function

Finding the Derivative of a Root Function Using the Limit Definition

Finding the Derivative of a Root Function Using the Limit Definition thumbnail
Using the limit definition to find the derivative of a square root function

Finding the nth Taylor Polynomial Exercise

Finding the nth Taylor Polynomial Exercise thumbnail
Finding the nth Taylor polynomial of the natural log function centered at 1
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