What you’ll learn to do: Apply the chain rule in a variety of situations

We have seen the techniques for differentiating basic functions ([latex]x^n, \, \sin x, \, \cos x[/latex], etc.) as well as sums, differences, products, quotients, and constant multiples of these functions. However, these techniques do not allow us to differentiate compositions of functions, such as [latex]h(x)= \sin (x^3)[/latex] or [latex]k(x)=\sqrt{3x^2+1}[/latex]. In this section, we study the rule for finding the derivative of the composition of two or more functions.