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8-43.

Differentiate.

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

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

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

$\frac { d } { d x }$ (k²9³^k⁻¹)
Hint (d):
We know that k is a variable (not a constant) because it appears in the $\frac{d}{dk}.$

$\frac { d } { d x }$ (sin²x cos x)
Hint (e):
Product Rule.

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