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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![### Calculus Problem: Differentiation
**Problem:**
Find the derivative of \( y \) with respect to \( x \) if \( y = e^{-3x} \).
**Solution:**
To solve for the derivative of \( y \) with respect to \( x \), we need to differentiate the given function.
\[ y = e^{-3x} \]
Applying the chain rule for differentiation:
\[ \frac{dy}{dx} = \frac{d}{dx} \left( e^{-3x} \right) \]
\[ = e^{-3x} \cdot \left( -3 \right) \]
Therefore,
\[ \boxed{\frac{dy}{dx} = -3e^{-3x}} \]
This is the derivative of \( y \) with respect to \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F108f85ec-5786-44dd-b590-51bf325bef20%2F1f9b8df3-f6b2-4133-b20c-d8001184b8fe%2Foxmtnk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Problem: Differentiation
**Problem:**
Find the derivative of \( y \) with respect to \( x \) if \( y = e^{-3x} \).
**Solution:**
To solve for the derivative of \( y \) with respect to \( x \), we need to differentiate the given function.
\[ y = e^{-3x} \]
Applying the chain rule for differentiation:
\[ \frac{dy}{dx} = \frac{d}{dx} \left( e^{-3x} \right) \]
\[ = e^{-3x} \cdot \left( -3 \right) \]
Therefore,
\[ \boxed{\frac{dy}{dx} = -3e^{-3x}} \]
This is the derivative of \( y \) with respect to \( x \).
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