### Home > APCALC > Chapter 3 > Lesson 3.4.2 > Problem3-165

3-165.

What is $\frac { d y } { d x }$ for each of the following functions? You will need to rewrite each equation first.

$\frac{dy}{dx}=y'(x)=\text{ derivative of the fundion } y \text{ when }x \text{ is the input variable.}$

1. $y = \sqrt [ 3 ] { \frac { 1 } { x ^ { 2 } } }$

Before differentiating, rewrite $y$ with a negative fractional exponent.

1. $y = x\sqrt { x }$

Before differentiating, rewrite $y$ with a fractional exponent.

1. $y = \sin^2(x) + \cos^2(x)$

Before differentiating, rewrite $y$. Think: trig identities!

1. $y = \large\frac { x + 2 } { x }$

Before differentiating, rewrite $y$ by simplifying the fraction and rewriting with a fractional exponent.