   Chapter 9.5, Problem 13E ### 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 11-20, find the indicated derivatives and simplify. d y d x  for  y = 1 − 2 x 2 x 4 − 2 x 2 + 5

To determine

To calculate: The derivative of the expression (12x2)(x42x2+5) with simplification.

Explanation

Given Information:

The provided expression is (12x2)(x42x2+5).

Formula Used:

The quotient rule:

If two functions are given in the form f(x)g(x), then the derivative is given as,

ddx(fg)=f.gg.fg2.

Calculation:

Consider the provided expression (12x2)(x42x2+5),

In the expression, the value of,

f(x)=(12x2)

And

g(x)=(x42x2+5)

Apply the quotient rule of the expression,

ddx(fg)=ddx(12x2).(x42x2+5)ddx(x42x2+5).(12x2)(x42x2+5)2

Evaluate the expression further,

ddx(fg)=(ddx(1)2ddx(x2)).(x42x2+5)(ddx(x4)2ddx(x2)+ddx(5))

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