Original
So far we have seen how to compute the derivative of a function built
up from other functions by addition, subtraction, multiplication and
division. There is another very important way that we combine
functions: composition. The {{CMD_7}}chain rule{{CMD_8}} allows us to deal with
this case. Consider
{{MATH_9}}
While there are several different ways to differentiate this function,
if we let {{MATH_10}} and {{MATH_11}}, then we can express
{{MATH_12}}. The question is, can we compute the derivative of a
composition of functions using the derivatives of the constituents
{{MATH_13}} and {{MATH_14}}? To do so, we need the {{CMD_15}}chain rule{{CMD_16}}.