BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

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

Answer to Problem 22E

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.

  df(a)dx=dfdadadx

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) .

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