# use part 1 of the fundamental theorem of calculus to find the derivative of the function.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 5.4, Problem 7E
To determine

## To find: use part 1 of the fundamental theorem of calculus to find the derivative of the function.

Expert Solution

The derivative of the function is g(x)=1x3+1

### Explanation of Solution

Given information: The function is g(x)=1x1t3+1

Let’s remind of the fundamental theorem of calculus part 1:

The fundamental theorem of calculus part 1: If f is continuous on [a,b] then the function of g defined by

g(x)=axf(t) dt where axb is continuous on [a,b] and differentiable on (a,b) and g(x)=f(x) .

Now given, g(x)=1x1t3+1

Differentiation with respect to x,

d g(x)dx=ddx[1x1t+31]

g(x)=1x3+1[ where g(x)=f(x) ]

Thus, g(x)=1x3+1

Hence, The derivative of the function is g(x)=1x3+1

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