CPM Homework Help : CALC3RD Problem 8-43

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Home > CALC3RD > Chapter Ch8 > Lesson 8.1.4 > Problem 8-43

8-43.

Differentiate.

$\frac { d } { d x } ( \frac { 6 x - 2 } { 3 x + 1 } )$
Hint (a):
Quotient Rule

$\frac { d } { d x } [ \operatorname { sec } ( 5 \operatorname { ln } [ x ] ) ]$
Hint (b):
$\frac{d}{dx}\sec(x)=\sec(x)\tan(x)$

$\frac { d } { d x } ( \frac { \operatorname { sin } ( 2 x ) } { x ^ { 3 } } )$
Step (c):
$=\frac{2x^{3}\text{cos}(2x)-3x^{2}\text{sin}(2x)}{x^{6}}$

$\frac { d } { d k } ( k ^ { 2 } 9 ^ { 3 k - 1 } )$
Hint (d):
We know that $k$ is a variable (not a constant) because it appears in the $\frac{d}{dk}$ .

$\frac { d } { d x } [ \operatorname { sin } ^ { 2 } ( x ) \operatorname { cos } ( x ) ]$
Hint (e):
Product Rule

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