Chain Rule

Definition: Let f(x) and g(x) be differentiable functions. Then  chain1.

Example: Find the derivative of h(x) = \sqrt{\sin(x)}

Solution:  We can split h(x) up into two functions, f(t) and g(x), where f(t) = \sqrt{t} and g(x) = \sin(x). First, we find the derivatives of each of these functions:

chain2

Then we apply the chain rule:

chain3

Note how we plugged g(x) in for t into f(t) in the first part of the formula.

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