Chapter 4.1, Problem 34E

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

Chapter
Section

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
Textbook Problem

# In Exercises 17-40, find the derivative of the given function. [HINT: See Example 1 and 2.] t ( x ) = 3 | x | − x

To determine

To calculate: The derivative of function t(x)=3|x|x.

Explanation

Given Information:

The provided function is t(x)=3|x|âˆ’x.

Formula used:

Difference rule of derivative, [fâˆ’g]â€²(x)=fâ€²(x)âˆ’gâ€²(x)

Constant multiple rule, fâ€²(cx)=cfâ€²(x) where c is constant.

Derivative of a function f(x)=xn with the help of power rule is fâ€²(x)=nxnâˆ’1.

Derivative of function f(x)=|x| is |x|x, where xâ‰ 0.

Calculation:

Consider the function, t(x)=3|x|âˆ’x.

Convert function to power form as,

t(x)=3|x|âˆ’x12

Apply difference rule of derivative,

tâ€²(x)=ddx(3|x|)âˆ’

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