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-3x If h (x) = ln(x + 4 + e−³ª), then h′ (0) =? 01/10 O nonexistent 0 210 210

-3x If h (x) = ln(x + 4 + e−³ª), then h′ (0) =? 01/10 O nonexistent 0 210 210

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...
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The image presents a calculus problem that involves finding the derivative of a logarithmic function at a specific point. **Problem Statement:** "If \( h(x) = \ln(x + 4 + e^{-3x}) \), then \( h'(0) = ? \)" **Answer Choices:** - \( \frac{1}{5} \) - nonexistent - \( -\frac{2}{5} \) - \( \frac{2}{5} \) No graphs or diagrams are present in the image.
Transcribed Image Text:The image presents a calculus problem that involves finding the derivative of a logarithmic function at a specific point. **Problem Statement:** "If \( h(x) = \ln(x + 4 + e^{-3x}) \), then \( h'(0) = ? \)" **Answer Choices:** - \( \frac{1}{5} \) - nonexistent - \( -\frac{2}{5} \) - \( \frac{2}{5} \) No graphs or diagrams are present in the image.
Expert Solution
Step 1: Introduction

This is question of differentiation

Here function given 

We have to differentiate it and put value given .

Further calculation is given below 

steps

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Solved in 3 steps

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