# Chain Rule

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

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:

Then we apply the chain rule:

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

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