How do I use the chain rule?
The chain rule is used to differentiate a function of a function. An example would be:y = exp [x2]The first step is to make a substitution for the 'internal function'. u = x2This leaves our function as:y = exp[u]We now differentiate the function and the substitution because:dy/dx = dy/du x du/dxdy/du = exp[u]du/dx = 2xWe multiply these two results for the reason shown above:dy/dx = 2x exp[u]The final step is to re-substitute for u:dy/dx = 2x exp[x2]
