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 34E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 34E

The derivative of the given function is dydx=4(x+x)x+2x+18(x+x+x)(x+x)x .

Explanation of Solution

Given:

The given function is y=x+x+x .

Calculation:

  y=x+x+x

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a12,a=x+x+x

  dydx=dda(a12)ddx(x+x+x)

Use derivative rule.

  ddx(xn)=nxn1 .

  dydx=12a[1+ddx(x+x)]

Substitute the value of a=x+x+x .

  dydx=12x+x+x[1+ddx(x+x)]

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a12,a=x+x

  dydx=12x+x+x[1+dda(a12)ddx(x+x)]

Use derivative rule.

  ddx(xn)=nxn1 .

  dydx=12x+x+x[1+12a(1+12x)]

Substitute the value of a=x+x .

  dydx=12x+x+x[1+12x+x(1+12x)]dydx=12x+x+x[1+2x+14(x+x)x]dydx=12x+x+x[4(x+x)x+2x+14(x+x)x]dydx=4(x+x)x+2x+18(x+x+x)(x+x)x

Hence the derivativeof the given function is dydx=4(x+x)x+2x+18(x+x+x)(x+x)x .

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