Main Ideas

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Here are the main points that are addressed in the video. Please read these and think about them as you watch.

The chain rule is used to differentiate the composition of two (or more) functions.
The derivative of the composition of two functions $f$ and $g$ is not the composition of their derivatives.
The derivative of the composite function $f \circ g (x)$ is the product of the derivative of $f$ with respect to $g(x)$ and the derivative of $g$ with respect to $x$ . Symbolically, $\dfrac {d}{dx} f \circ g (x) = f'(g(x)) \times g'(x)$ .