Chapter 9.5, Problem 15E

### 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 z d x  for  z = x 2 + x 2 1 − x − 2 x 2

To determine

To calculate: The derivative of the expression x2+(x2)(1x2x2) with simplification.

Explanation

Given Information:

The provided expression is x2+(x2)(1âˆ’xâˆ’2x2).

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 x2+(x2)(1âˆ’xâˆ’2x2),

The derivative of x2 is as follows:

fâ€²1(x)=ddx(x2)=2x

For the derivative of (x2)(1âˆ’xâˆ’2x2), follow the steps:

In the expression, the value of,

f(x)=(x2)

And

g(x)=(1âˆ’xâˆ’2x2)

Apply the quotient rule of the expression,

f2â€²=ddx(fg)=ddx(x2).(1âˆ’xâˆ’2x2)âˆ’ddx(1âˆ’xâˆ’2x2).(x2)(1âˆ’xâˆ’2x2)2

Evaluate the expression further,

ddx(fg)=(ddx(x2)).(1âˆ’xâˆ’2x2)âˆ’(ddx(1)âˆ’ddx(x)âˆ’2ddx(x2))

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