# 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 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:

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

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

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

Another example: The chain rule can be used more than once. (That’s what makes the “chain” in the “chain rule”!)

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

Download ppt "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."

Similar presentations