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CHAIN
RULE A
frequently used rule in differential calculus is the chain rule. This rule
links together derivatives that have related variables. The chain rule is
where the variable y = f(u) is a differentiable function
of u and u = g(x) is a differentiable function of x. EXAMPLE: Find the derivative of
SOLUTION. Let
and _{ } Then,
and
Now,
and substituting into equation (1) gives
but,
Therefore,
EXAMPLE: Find
where
and
SOLUTION. By the chain rule
and
Then,
and by substitution
PRACTICE PROBLEMS: Find
in the following:
ANSWERS:

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