
Home > CALC > Chapter 3 > Lesson 3.2.3 > Problem 3-73
3-73.
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.