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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Question
![**Find the Derivative of the Function**
Given: \( y = e^{22x} \)
---
**What Rule Should Be Used to Differentiate?**
A. \( \frac{d}{dx} [e] = 0 \)
B. \( \frac{d}{dx} \left[ e^{g(x)} \right] = e^{g(x)} g'(x) \) ✅
C. \( \frac{d}{dx} \left[ a^x \right] = (\ln a) a^x \)
D. \( \frac{d}{dx} \left[ e^x \right] = e^x \)
---
**The Derivative of \( y \) with Respect to \( x \) if \( y = e^{22x} \) is \(\_\_\_\_\)**
This question involves finding the derivative of the exponential function \( e^{22x} \). Option B is the correct rule to differentiate an exponential function of the form \( e^{g(x)} \), where \( g(x) = 22x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae259756-8f06-4e5c-ae2d-b16c40451d6f%2F06f01a28-9141-4f99-91fa-abf93d09606e%2Fhu0y71n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Derivative of the Function**
Given: \( y = e^{22x} \)
---
**What Rule Should Be Used to Differentiate?**
A. \( \frac{d}{dx} [e] = 0 \)
B. \( \frac{d}{dx} \left[ e^{g(x)} \right] = e^{g(x)} g'(x) \) ✅
C. \( \frac{d}{dx} \left[ a^x \right] = (\ln a) a^x \)
D. \( \frac{d}{dx} \left[ e^x \right] = e^x \)
---
**The Derivative of \( y \) with Respect to \( x \) if \( y = e^{22x} \) is \(\_\_\_\_\)**
This question involves finding the derivative of the exponential function \( e^{22x} \). Option B is the correct rule to differentiate an exponential function of the form \( e^{g(x)} \), where \( g(x) = 22x \).
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