# The differentiation of the given 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 3.1, Problem 23E
To determine

## To find:The differentiation of the given function

Expert Solution

Differentiating the function is dydt=15t45+10(t)52t4

### Explanation of Solution

Given:

The function is

f(t)=t5+4t5

Concept used:

Definition of the differentiation:-Differentiation is the action of computing a derivative

The derivative of a function y=f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to x

Calculation:

The function

f(t)=t5+4t5...................(1)

The derivative of a function

y=f(x)y=f(x)=dydx

Differentiating the equation (1) with respect to t

dydt=ddt(t5+4t5)dydt=ddt(t5)+4ddtt5dydt=15t45+42(t5)125t4dydt=15t45+10(t)52t4

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