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
![**Problem Statement**
Find the derivative of the function.
\[ y = 3e^{4x^2 - 3} \]
---
**Solution**
\[ \frac{dy}{dx} = \ \boxed{\ } \]
**Explanation:**
To solve this problem, you need to find the derivative of the given function with respect to \(x\). The function involves an exponential term, where the exponent is a function of \(x\), i.e. \(4x^2 - 3\). To differentiate this, apply the chain rule.
Remember, for a function of the form \(y = e^{u}\), the derivative is \(\frac{dy}{dx} = e^{u} \cdot \frac{du}{dx}\).
In this case, \(u = 4x^2 - 3\), so find \(\frac{du}{dx}\).
Finally, does not forget to multiply by the coefficient 3 in the original function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae259756-8f06-4e5c-ae2d-b16c40451d6f%2Fcc8f42a8-9e63-4775-badf-f063823186a3%2F89a6kuc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Find the derivative of the function.
\[ y = 3e^{4x^2 - 3} \]
---
**Solution**
\[ \frac{dy}{dx} = \ \boxed{\ } \]
**Explanation:**
To solve this problem, you need to find the derivative of the given function with respect to \(x\). The function involves an exponential term, where the exponent is a function of \(x\), i.e. \(4x^2 - 3\). To differentiate this, apply the chain rule.
Remember, for a function of the form \(y = e^{u}\), the derivative is \(\frac{dy}{dx} = e^{u} \cdot \frac{du}{dx}\).
In this case, \(u = 4x^2 - 3\), so find \(\frac{du}{dx}\).
Finally, does not forget to multiply by the coefficient 3 in the original function.
Expert Solution
Step 1: Derivative property used :
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