# The derivative of the given function by using definition of 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 30E

a.

To determine

## To calculate:The derivative of the given function by using definition of derivative.

Expert Solution

Derivative of the function is .

### Explanation of Solution

Given: f(x)=x+1/x

Concept used:

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

f(x)=x+1/x be a given function.

It has to find derivative of the function.

f(x)=x+1/x

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

f'(x)=limh0(x+h)+1/(x+h)x+1/xh=limh0(x+h)2+1x21x(x+h)h=limh0x2+h2+2xh+1x21x(x+h)×1h

=limh0h2+2xhx(x+h)×1h=limh0h+2xx(x+h)[00]apply L.hospital rule=22x=1x=

Hence, derivative of the function is .

b.

To determine

Expert Solution

### Explanation of Solution

Given: f(x)=x+1/x

Concept used:

Definition of derivative: f'(x)=df(x)dx

f(x)=x+1/x be a given function.

It has to find derivative of the function.

f(x)=x+1/x

f'(x)=df(x)dx

f'(x)=d(x+1/x)dx=11x2

Now the graph of function and graph of the derivative is

Respectively.

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