   Chapter 9.5, Problem 16E ### 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 = 200 x − 100 x 3 x + 1

To determine

To calculate: The derivative of the expression 200x(100x)(3x+1) with simplification.

Explanation

Given Information:

The provided expression is 200x(100x)(3x+1).

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 is 200x(100x)(3x+1),

The derivative of 200x is as follows:

f1(x)=ddx(200x)=200

For the derivative of (100x)(3x+1), follow the steps:

In the expression, the value of,

f(x)=(100x)

And

g(x)=3x+1

Apply the quotient rule of the expression,

f2=ddx(fg)=ddx(100x).(3x+1)ddx(3x+1).(100x)(3x+1)2

Evaluate the expression further,

ddx(fg)=(100ddx(x)).(3x+1)(3ddx(x)+ddx(1))

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