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 \(\frac{d}{dx} \left(2^x\right)\). Type ln(x) for the natural logarithm function.
---
**Instructions for Solution:**
To differentiate \(2^x\), use the formula for the derivative of an exponential function:
\[
\frac{d}{dx} \left(a^x\right) = a^x \ln(a)
\]
In this case, \(a = 2\), so:
\[
\frac{d}{dx} \left(2^x\right) = 2^x \ln(2)
\]
Type "ln(x)" when using the natural logarithm function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86aaa619-fdff-47f7-a0f1-75f1e68fb632%2Fe1cfcf39-5f9c-4b1c-815d-364930457881%2F52c0obe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \(\frac{d}{dx} \left(2^x\right)\). Type ln(x) for the natural logarithm function.
---
**Instructions for Solution:**
To differentiate \(2^x\), use the formula for the derivative of an exponential function:
\[
\frac{d}{dx} \left(a^x\right) = a^x \ln(a)
\]
In this case, \(a = 2\), so:
\[
\frac{d}{dx} \left(2^x\right) = 2^x \ln(2)
\]
Type "ln(x)" when using the natural logarithm function.
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