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.

$y = f(g(x))$ is a composite function. This means that the outputs of the function $g$ become the inputs of the function $f$ .
The derivative of the function $y = f(x)$ at $x = a$ conveys how many times as large a very small change in $y$ is compared to the corresponding small change in $x$ away from $x = a$ .
Developing a method for computing the derivative of the composite function $y = f(g(x))$ requires determining how much $f(g(x))$ changes when $x$ changes by a very small amount.
The derivative of the composite function $y = f(g(x))$ is $f'(g(x)) \times g'(x)$ .