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2.4 The Chain Rule If f and g are both differentiable and F is the composite function defined by F(x)=f(g(x)), then F is differentiable and F is given.

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Presentation on theme: "2.4 The Chain Rule If f and g are both differentiable and F is the composite function defined by F(x)=f(g(x)), then F is differentiable and F is given."— Presentation transcript:

1 2.4 The Chain Rule If f and g are both differentiable and F is the composite function defined by F(x)=f(g(x)), then F is differentiable and F is given by the product In Leibniz notation, if y=f(u) and u=g(x) are both differentiable functions, then

2 Example: A faster way to write the solution: Differentiate the outer function... …then the inner function

3 Another example: derivative of the outer function derivative of the inner function It looks like we need to use the chain rule again!

4 Another example: The chain rule can be used more than once. (Thats what makes the chain in the chain rule!)

5 The Power Rule combined with the Chain Rule If n is any real number and u=g(x) is differentiable, then Alternatively, Example:


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