For each of the following functions, what is $f^\prime(x)$?

1. $f (x) = \cot(5x^2 - 2x)$

   Hint (a):

   Recall that $\frac{d}{dx}\cot(x)=-\csc^{2}(x).$

2. $f(x)=\frac{1}{\cot(x^4)}$

   Hint (b):

   Before differentiating, rewrite the expression.

   Hint (b):

   Note that $\cot(x^4) ≠ \cot^4(x)$.