Homework Help is Here – Start Your Trial Now!
Math
Calculus
2. The derivative of e) is e9(=) .g'(r). Use this to find the derivative of the following: (a) e- (b) e CON I

2. The derivative of e) is e9(=) .g'(r). Use this to find the derivative of the following: (a) e- (b) e CON I

Calculus: Early Transcendentals
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...
See similar textbooks
Question

2. The derivative of e
g(x)
is e
g(x)
· g
0
(x). Use this to find the derivative of the following:
(a) e
4x
2−x
(b) e
cos x

**Problem 2: Derivatives of Exponential Functions** Given that the derivative of \( e^{g(x)} \) is \( e^{g(x)} \cdot g'(x) \), use this formula to find the derivative of the following expressions: (a) \( e^{4x^2-x} \) (b) \( e^{\cos x} \) --- Explanation: This problem involves finding the derivatives of exponential functions with variable exponents using the chain rule. The chain rule states that if a function is composed of multiple functions, the derivative is the product of the derivative of the outer function and the derivative of the inner function. Here, we apply this concept to exponential functions where the exponent itself is a function of \( x \).
Transcribed Image Text:**Problem 2: Derivatives of Exponential Functions** Given that the derivative of \( e^{g(x)} \) is \( e^{g(x)} \cdot g'(x) \), use this formula to find the derivative of the following expressions: (a) \( e^{4x^2-x} \) (b) \( e^{\cos x} \) --- Explanation: This problem involves finding the derivatives of exponential functions with variable exponents using the chain rule. The chain rule states that if a function is composed of multiple functions, the derivative is the product of the derivative of the outer function and the derivative of the inner function. Here, we apply this concept to exponential functions where the exponent itself is a function of \( x \).
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS