CPM Homework Help : APCALC Problem 3-165

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3-165.

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

Hint:

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

$y = \sqrt [ 3 ] { \frac { 1 } { x ^ { 2 } } }$
Hint (a):
Before differentiating, rewrite $y$ with a negative fractional exponent.

$y = x\sqrt { x }$
Hint (b):
Before differentiating, rewrite $y$ with a fractional exponent.

$y = \sin^2(x) + \cos^2(x)$
Hint (c):
Before differentiating, rewrite $y$ . Think: trig identities!

$y = \large\frac { x + 2 } { x }$
Hint (d):
Before differentiating, rewrite $y$ by simplifying the fraction and rewriting with a fractional exponent.

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