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.
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We differentiate
and
and substitute them into The Chain Rule:
Example: Differentiate
Now just multiply the differentiated terms:
Our final answer must be in terms of
Hence we substitute
The final answer is
\[e^(2x-1)\]
Now just multiply the differentiated terms:
Our final answer must be in terms ofHence we substitute
The 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 substitute
The final answer is
