Since most derivatives are trivial to take, it's understandable why integrals get most of the mathematical tricksters' attention. However, not all derivatives are trivial to take and I think it's good to have as many tricks up your sleeves as possible. I noticed the other day that $\left(\frac{dy}{dx}\right)^{-1}=\frac{dx}{dy}$ and that we can use this fact to differentiate functions like the inverse trig functions e.g. $y=\arcsin(x)$, $$\frac{d \sin(y)}{dy}=\cos(y)=\cos(\arcsin(x))=\sqrt{1-x^2}=\left(\frac{dy}{dx}\right)^{-1}$$ My question is, does anybody know of any similar tricks to differentiate those rare functions which are non-trivial?