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3-73.
  1. Given f(x) below, find f ′(x). Homework Help ✎

    1. f(x) = −x3

    2. f(x) = 3 sin(x + π)

Use the Power Rule.

f(x) can be rewritten with a negative exponent.

f(x) can be rewritten with a fractional exponent.

You know that the derivative of y = sinx is y' = cosx. Well, f(x) is a transformation of y = sinx. So f '(x) (its slope function) will be a transformation of cosx.

The 3 represents a vertical stretch. How will that transform the derivative (slope) of y = sinx? The +π represents a horizontal shift. How will that transform the derivative (slope) of y = sinx?

The derivative will also be shifted π units to the left and stretched by a factor of 3.