Calculus 3.6

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The Chain Rule
3.6
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U.S.S. Alabama Mobile, Alabama
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We now have a pretty good list of shortcuts to
find derivatives of simple functions.
Of course, many of the functions that we will
encounter are not so simple. What is needed is a
way to combine derivative rules to evaluate more
complicated functions.
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Consider a simple composite function
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and another
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and one more
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Chain Rule
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We could also do it this way
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Here is a faster way to find the derivative
Differentiate the outside function...
then the inside function
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Another example
It looks like we need to use the chain rule again!
derivative of the outside function
derivative of the inside function
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Another example
(Thats what makes the chain in the chain
rule!)
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Derivative formulas include the chain rule!
etcetera
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The most common mistake on the chapter 3 test is
to forget to use the chain rule.
Every derivative problem could be thought of as a
chain-rule problem
The derivative of x is one.
derivative of outside function
derivative of inside function
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The chain rule enables us to find the slope of
parametrically defined curves
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Example
These are the equations for an ellipse.
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Dont forget to use the chain rule!
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