### Home > CALC > Chapter 4 > Lesson 4.1.2 > Problem 4-20

4-20.

Differentiate each function below. That is, find its slope function,

*f*′(*x*). Homework Help ✎*f*(*x*) = 6(*x*− 2)^{3}*f*(*x*) = 2 sin*x**f*(*x*) = (*x*+ 5)(2*x*− l)

You could expand *f*(*x*) before you differentiate. Or...

Strategy 1: *f* '(*x*) = 18*x*² − 72*x* + 72

Strategy 2: *f* '(*x*) = 18(*x* − 2)²

You know that the derivative of *y* = (*x* − 2)³ is *y* ' = 3(*x* − 2)². What about the vertical stretch of 6? If the *f*(*x*) is stretched by a factor of 6, what happens to its slopes/derivative? Are they stretched as well?

What does the 2 do to a sine graph? How will this affect the slope function?

Before you differentiate, expand *f*(*x*).

Before you differentiate, simplify *f*(*x*). But, don't forget that there was once a 0 in the denominator... be sure to restrict the domain of the derivative.