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Chapter 9.6, Problem 20E
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### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Mathematical Applications for the ...

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

# Differentiate the functions in Problems 3-20. y = 2 x − 1 − x 2

To determine

To calculate: The derivative of the function y=2x1x2.

Explanation

Given Information:

The provided function is y=2xâˆ’1âˆ’x2.

Formula used:

Power rule for a real number n is such that, if y=un then dydx=nunâˆ’1â‹…dudx, where u is a differentiable function of 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).

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

If any nonzero real number a has a negative integer n as its exponent then aâˆ’n=1an.

Calculation:

Consider the function,

y=2xâˆ’1âˆ’x2

Rearrange the function as,

y=12(2xâˆ’1âˆ’x)

Consider (2xâˆ’1) to be u,

y=12(uâˆ’x)

Differentiate both sides with respect to x,

yâ€²=ddx[12(uâˆ’x)]=12[ddx(u1/2)âˆ’ddx(x1/2

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