Some mneumonics:
The derivative of a cofunction can be derived from the derivative of the
original function:
If $\text{co}f(x) = f\left(\frac{\pi}{2} - x\right)$,
then $(\text{co}f)'(x) = -f'\left(\frac{\pi}{2} - x\right)$ by chain rule,
so the derivative is the negative with all functions replaced by cofunctions.

Hence since $\sin' = \cos$, we see that $\cos' = - co(\cos)=-\sin$,
and $\cot' = -\csc^2$,
and $\csc' = -\csc \cot$.

This is not deep and meaningful, but it's a good mneumonic if you \emph{must}
remember these.
