# The derivative of the given function by definition of derivative and state the domain of the function and the domain of its 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 2.7, Problem 26E
To determine

## To find:The derivative of the given function by definition of derivative and state the domain of the function and the domain of its derivative.

Expert Solution

Derivative of the function is 0 .

Domain of the function is 32 and domain of derivative is set of real number.

### Explanation of Solution

Given: f(x)=x222x3

Concept used:

Definition of derivative: f'(x)=limh0f(x+h)f(x)h

f(x)=x222x3 be a given function.

It has to find derivative of the function.

f(x)=x222x3

f'(x)=limh0f(x+h)f(x)h

f'(x)=limh0(x+h)222(x+h)3x222x3h=limh0(x+h)222(x+h)3x222x3×1h=limh0((x+h)22)(2x3)(x22)(2x+2h3)(2x+2h3)(2x3)×1h=limh0(x2+h2+2xh2)(2x3)(x22)(2x+2h3)(2x+2h3)(2x3)×1h=limh02x3+2h3+6x2h6x3x23h26xh+6(2x3+2hx23x24x4h+6)(2x+2h3)(2x3)×1h

=limh02h3+4x2h2x3h26xh+4h(2x+2h3)(2x3)×1h

=limh02h2+4x22xh3h6x+4(2x+2h3)(2x3)=limh02h(h+2x2hxh2323xh+2h)2h(xh+132h)(xh32h)=limh0(h+2x2hxh2323xh+2h)(xh+132h)(xh32h)=0

Domain of the function is the set of all possible input of the function, so here domain of the function is 32

Domain of the derivative is the set of all points in the domain of function at which function is differentiable.

Hence, domain of derivative and domain of function both are set of real number.

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