Chapter 9.5, Problem 18E

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# In Problems 11-20, find the indicated derivatives and simplify. d y d x  for  y = 2 x − 1 1 − 4 x 3

To determine

To calculate: The derivative of the expression 2x114x3 with simplification.

Explanation

Given Information:

The provided expression is 2xâˆ’11âˆ’4x3.

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)=fâ€².gâˆ’gâ€².fg2.

Calculation:

Consider the provided expression 2xâˆ’11âˆ’4x3,

For the derivative of 2xâˆ’11âˆ’4x3, follow the steps:

In the expression, the value of,

f(x)=2xâˆ’1

And

g(x)=1âˆ’4x3

Apply the quotient rule of the expression,

ddx(fg)=ddx(2xâˆ’1).(1âˆ’4x3)âˆ’ddx(1âˆ’4x3).(2xâˆ’1)(1âˆ’4x3)2

Evaluate the expression further,

ddx(fg)=(2ddq(x)âˆ’ddx(1)).(1âˆ’4x3)âˆ’(ddx(1)âˆ’4ddx(x3))

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