Do NOT use the quotient rule (though it will work). This is a Power Rule problem: $y = −2x^{−3}$. Reserve the Quotient Rule for situations in which there are variables in BOTH the numerator and the denominator.

Chain Rule.

This is not technically a Chain Rule problem, though you may use it.

This calls for the Quotient Rule.

$g'(x)=\frac{-\text{sin}x(x-3)^{8}-8\text{cos}x(x-3)^7}{(x-3)^{16}}$

Product Rule & Chain Rule combined.

Refer to the hint in part (a). And recall that the reciprocal of $\operatorname{cos}x$ is $\operatorname{sec}x$.