CPM Homework Help : APCALC Problem 7-133

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Home > APCALC > Chapter 7 > Lesson 7.3.3 > Problem 7-133

7-133.

Compute the following derivatives.

$\frac { d } { d x } [ \operatorname { sin } ^ { 3 } ( x ) ]$
Hint (a):
$\sin^3(x) = (\sin(x))^3$

$\frac { d } { d k } [ \sqrt [ 3 ] { 7 + 4 k - 2 k ^ { 2 } } ]$
Hint (b):
$\sqrt[3]{7+4k-2k^{2}}=(7+4k-2k^{2})^{1/3}$
Answer (b):
$\frac{1}{3}(7+4k-2k^{2})^{-2/3}(4-4k)$

$\frac { d } { d x } [ \pi ^ { x } x ^ { \pi } ]$
Hint (c):
$\text{Use the Product Rule. Also, }\frac{d}{dx}a^{x}=\text{ln}(a)\cdot a^{x}.$

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