Differentiation - The Chain Rule

If we have to differentiate a function which consists of one operation carried out after another we have to use the chain rule. Several examples are shown below together with the constituent functions which we call u and v.

Function

We differentiateandand substitute them into The Chain Rule:

Example: Differentiate

Now just multiply the differentiated terms:

Our final answer must be in terms ofHence we substituteThe final answer is

Example:Differentiate  
\[e^(2x-1)\]

Now just multiply the differentiated terms:

Our final answer must be in terms ofHence we substituteThe final answer is

Example: Differentiate 1 over {x^2+2}

Now just multiply the differentiated terms:

Our final answer must be in terms ofHence we substituteThe final answer is