Please explain with steps and what formula to use ### Problem Statement:**9)** $ y = 5x^2 e^{3x} $Select the correct derivative of the function from the options below:**A)** $ 5xe^{3x}(2x + 3) $**B)** $ 10xe^{3x}(3x + 2) $**C)** $ 5xe^{3x}(3x + 2) $**D)** $ 10xe^{3x}(2x + 3) $### Explanation:The problem asks for the derivative of the given function $ y = 5x^2 e^{3x} $. The options listed are potential derivatives of this function. The task involves identifying the correct option by applying the rules of differentiation, such as the product rule and the chain rule.Here’s a step-by-step guide to find the solution:1. Recognize that the function is a product of two functions: $ u = 5x^2 $ and $ v = e^{3x} $.2. Apply the product rule: $ \frac{d}{dx}(uv) = u'v + uv' $.3. Differentiate $ u = 5x^2 $ to get $ u' = 10x $.4. Differentiate $ v = e^{3x} $ using the chain rule to get $ v' = 3e^{3x} $.5. Substitute these derivatives into the product rule formula.This solution will help find the correct option from A, B, C, or D.

Answered: 9) y = 5x²e3x A) 5xe3x(2x + 3) C)…

Math

Calculus

9) y = 5x²e3x A) 5xe3x(2x + 3) C) 5xe3x(3x + 2) B) 10ex3x(3x + 2) D) 10xe3x(2x + 3) 1

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Please explain with steps and what formula to use

### Problem Statement:

**9)** $ y = 5x^2 e^{3x} $

Select the correct derivative of the function from the options below:

**A)** $ 5xe^{3x}(2x + 3) $

**B)** $ 10xe^{3x}(3x + 2) $

**C)** $ 5xe^{3x}(3x + 2) $

**D)** $ 10xe^{3x}(2x + 3) $

### Explanation:

The problem asks for the derivative of the given function $ y = 5x^2 e^{3x} $. The options listed are potential derivatives of this function. The task involves identifying the correct option by applying the rules of differentiation, such as the product rule and the chain rule.

Here’s a step-by-step guide to find the solution:
1. Recognize that the function is a product of two functions: $ u = 5x^2 $ and $ v = e^{3x} $.
2. Apply the product rule: $ \frac{d}{dx}(uv) = u'v + uv' $.
3. Differentiate $ u = 5x^2 $ to get $ u' = 10x $.
4. Differentiate $ v = e^{3x} $ using the chain rule to get $ v' = 3e^{3x} $.
5. Substitute these derivatives into the product rule formula.

This solution will help find the correct option from A, B, C, or D.

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