### Home > APCALC > Chapter 3 > Lesson 3.2.3 > Problem3-73

3-73.

Given each function below, write an equation for $f^\prime$.

1. $f(x) = −x^3$

Use the Power Rule.

1. $f(x) = \frac { 1 } { x ^ { 2 } }$

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

1. $f(x) = \sqrt { 2 }$

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

1. $f(x)=3\sin(x+\pi)$

You know that the derivative of $y=\sin x$ is $y^\prime =\cos x$. Well, $f(x)$ is a transformation of $y=\sin x$. So $f^\prime (x)$ (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 $3$.