   Chapter 11.1, Problem 33E ### 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 = [ ln ( x 4 + 2 ) ] 2

To determine

To calculate: The value of y for the function y=[ln(x4+3)]2.

Explanation

Given Information:

The provided function is y=[ln(x4+3)]2.

Formula Used:

Chain rule for function f(x)=u(v(x)) is f(x)=u(v(x))v(x).

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

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

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

Calculation:

Consider the function, y=[ln(x4+3)]2.

Differentiate with respect to x,

dydx=ddx{[ln(x4+3)]2}

Use chain rule of derivatives,

dydx=2[ln(<

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