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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**Finding the Derivative of the Function**
Given the function:
\[ y = 2e^x + x^2 \]
we are tasked with finding its derivative.
---
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To compute the derivative of the given function, apply the sum and power rules of differentiation.
1. Identify and individually differentiate each term.
- The term \( 2e^x \):
\[ \frac{d}{dx}(2e^x) = 2e^x \]
- The term \( x^2 \):
\[ \frac{d}{dx}(x^2) = 2x \]
2. Combine the differentiated results:
\[ \frac{d}{dx}(2e^x + x^2) = 2e^x + 2x \]
Therefore, the derivative of the function \( y = 2e^x + x^2 \) is:
\[ y' = 2e^x + 2x \]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F500c0e80-687a-4e1b-8f8e-54233bb713dd%2F66c3e1bf-599b-48bb-b636-7f15a4f82b8a%2Fiuq5w99_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Finding the Derivative of the Function**
Given the function:
\[ y = 2e^x + x^2 \]
we are tasked with finding its derivative.
---
Note: There is an image insert and formatting toolbar visible, which suggests this content is editable within a text editor. The toolbar includes options for inserting media, links, formatted text, and more.
To compute the derivative of the given function, apply the sum and power rules of differentiation.
1. Identify and individually differentiate each term.
- The term \( 2e^x \):
\[ \frac{d}{dx}(2e^x) = 2e^x \]
- The term \( x^2 \):
\[ \frac{d}{dx}(x^2) = 2x \]
2. Combine the differentiated results:
\[ \frac{d}{dx}(2e^x + x^2) = 2e^x + 2x \]
Therefore, the derivative of the function \( y = 2e^x + x^2 \) is:
\[ y' = 2e^x + 2x \]
---
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