# Find the derivative 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 3.4, Problem 22E
To determine

## Find the derivative of the given function.

Expert Solution

The derivative of the given function is dydx=2xe(1x2)ln(10)ln(10) .

### Explanation of Solution

Given:

The given function is y=101x2 .

Calculation:

Use exponent rule xy=eyln(x) .

y=101x2101x2=e(1x2)ln(10)y=e(1x2)ln(10)

Apply chain rule.

Let f=ea,a=(1x2)ln(10)

dydx=dda(ea)ddx[(1x2)ln(10)]

Use derivative rule.

ddx(ex)=exandddx(xn)=nxn1 .

dydx=ea[2xln(10)]dydx=2xealn(10)

Substitute the value of a=(1x2)ln(10) .

dydx=2xe(1x2)ln(10)ln(10)

Hence the derivativeof the given function is dydx=2xe(1x2)ln(10)ln(10) .

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!