### Home > CALC > Chapter Ch3 > 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* = sin*x* is *y*' = cos*x*. Well, *f*(*x*) is a transformation of *y* = sin*x*. So *f* '(*x*) (its slope function) will be a transformation of cos*x*.

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

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