Chapter 9, Problem 79RE

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 79 and 80, find the second derivatives. y = x − x 2

To determine

To calculate: The second derivative of the function y=xx2.

Explanation

Given Information:

The provided function is y=xâˆ’x2.

Formula used:

Difference rule for function f(x)=u(x)âˆ’v(x), where u and v are differentiable functions of x, then fâ€²(x)=uâ€²(x)âˆ’vâ€²(x).

Power of x rule for function f(x)=xn is fâ€²(x)=nxnâˆ’1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Calculation:

Consider the function,

y=xâˆ’x2

Rewrite the function as,

y=x1/2âˆ’x2

Differentiate both sides with respect to x,

dydx=ddx(x1/2âˆ’x2)yâ€²=ddx(x1/2)âˆ’ddx(x2)

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