find y^'. y=5 x e^3 x

Name: Problem 51, Chapter 3: Calculus, Early Transcendentals
Uploaded: 2021-07-24T19:00:05-08:00
Duration: 2 min 32 s
Channel: Eric Mockensturm
Description: find y^'. y=5 x e^3 x

step 1 And these three problems, we need to use the product rule as well as the chain rule. So we have,

Question

find $y^{\prime}$. $y=5 x e^{3 x}$

   find $y^{\prime}$.  $y=5 x e^{3 x}$

Calculus, Early Transcendentals

Michael Sullivan,… 1st Edition

Chapter 3, Problem 51

Instant Answer

Solved by Expert Eric Mockensturm

07/24/2021

Step 1

We need to find the derivative of this function. We can see that this function is a product of two functions, $5x$ and $e^{3x}$. So, we will use the product rule to find the derivative. The product rule states that the derivative of a product of two functions is Show more…

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find $y^{\prime}$. $y=5 x e^{3 x}$

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Key Concepts

Product Rule

The product rule is used to differentiate functions that are the product of two or more functions. It states that the derivative of the product of two functions is the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first function.

Chain Rule

The chain rule is used for differentiating composite functions. When a function is composed with another function, the derivative of the composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.

Constant Multiple Rule

The constant multiple rule states that if a function is multiplied by a constant, its derivative is that constant multiplied by the derivative of the function. This simplifies the differentiation process by allowing you to factor out any constants before taking the derivative.

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