Find f'(x). f(x) = 4 ex + 5x - In x f'(x) =

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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**Problem Statement:**

Find \( f'(x) \).

Given:  
\[ f(x) = 4e^x + 5x - \ln x \]

**Objective:**

Calculate the derivative \( f'(x) \) of the function provided.

**Solution Framework:**

To find \( f'(x) \):  
1. Differentiate \( 4e^x \).  
2. Differentiate \( 5x \).  
3. Differentiate \( -\ln x \). 

Combine these derivatives to obtain the result:
\[ f'(x) = 4e^x + 5 - \frac{1}{x} \]

**Answer:**

\[ f'(x) = \boxed{4e^x + 5 - \frac{1}{x}} \]
Transcribed Image Text:**Problem Statement:** Find \( f'(x) \). Given: \[ f(x) = 4e^x + 5x - \ln x \] **Objective:** Calculate the derivative \( f'(x) \) of the function provided. **Solution Framework:** To find \( f'(x) \): 1. Differentiate \( 4e^x \). 2. Differentiate \( 5x \). 3. Differentiate \( -\ln x \). Combine these derivatives to obtain the result: \[ f'(x) = 4e^x + 5 - \frac{1}{x} \] **Answer:** \[ f'(x) = \boxed{4e^x + 5 - \frac{1}{x}} \]
Expert Solution
Step 1

Topic- Derivative of a function

We are given,

f(x)=4ex+5x-ln(x)

we know that,ddxex=exddxxn=nxn-1ddxln(x)=1x

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