Download presentation

Presentation is loading. Please wait.

Published byMia Foley Modified over 2 years ago

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:

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google