Differentiability and the Chain Rule

When a function has a well-defined derivative, and how to differentiate a function within a function.

Differentiability

A function is differentiable at a point if its derivative exists there. Every differentiable function is continuous, but not every continuous function is differentiable.

Chain Rule

For a composite function $y = f(g(x))$:

$$\frac{dy}{dx} = f'(g(x)) \cdot g'(x)$$
Lesson 12 of 32
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