Say$f(x)=\mathrm{ln}(1+2x+2{x}^{2})$ or $g(x)=\mathrm{tan}(2{x}^{4}-x)$.Using the definition leads to messy derivatives almost immediately.If it was some simple rational function,for example,i would try to use Maclaurin Series of $\frac{1}{1+x}$ or $\frac{1}{1-x}$ and then manipulate it to get result