# Tofind: the function using its first derivative.

### 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 4, Problem 54RE
To determine

## Tofind:the function using its first derivative.

Expert Solution

Thefunction using its first derivative f(u)=u22+2u12+12.

### Explanation of Solution

Given:

f(u)=u2+uu, f(1)=3. .

Concept used:

Antiderivative=integration

f(t)dt=f(t) . Or dydtdt=y .

Since, the multiplication of two operators ×ddt=1 .

Integration formula:

xndx=xn+1n+1 .

Calculation:

f(u)=u2+uu, f(1)=3. .

f(u)du=u2+uudu, f(1)=3. .

f(u)=udu+1udu, f(1)=3.

f(u)=u22+u12du, f(1)=3.

f(u)=u22+u1212+C, f(1)=3.

f(u)=u22+2u12+C, f(1)=3.

3=122+2(1)12+C.

3=12+2+C.

12=C .

f(u)=u22+2u12+12.

Hence the function using its first derivative f(u)=u22+2u12+12.

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