   Chapter 11.1, Problem 38E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 25-38, find y'. y = log 2 ( 1 − x − x 2 )

To determine

To calculate: The value of y for the function y=log2(1xx2).

Explanation

Given Information:

The provided function is y=log2(1xx2).

Formula Used:

The change of base formula is such that, for logbM=logaMlogab, where a, b are the base of logarithm and M is any positive number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Derivative of natural logarithmic functions is such that, if y=lnu, where u is a differentiable function of x then dydx=1ududx.

Calculation:

Consider the function, y=log2(1xx2)

Use the change of base property of logarithms,

y=ln(1xx2)ln2

Differentiate with respect to x,

dydx=ddx[ln(1<

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