By: Susana Cardona & Demetri Cheatham © Cardona & Cheatham 2011

 Slope of a tangent line  Six different techniques: Chain rule, product rule, Quotient rule, E.T.A, Implicit differentiation and Logs.

Chain Rule Bring exponent down in front of the variable, if it’s a coefficient multiply exponent. Then subtract one from the exponent and go back in and take a derivative.

Example

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Solution

Product Rule  First write the problem times derivative of the second problem plus write the second problem times the derivative of the first problem.  FDS+SDF

Example    

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Solution 

Quotient Rule Write the bottom times the derivative of the top minus write the top times the derivative of the bottom over the bottom squared

Example

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Solution

 Bring down exponent, multiply coefficient if there’s one, and write the trig and the angle times the derivative of the trig times the derivative of the angle

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N ATURAL L OG 1 over the angle times the derivative of the angle

E XAMPLE

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S OLUTION

Implicit Is almost the same as a chain rule but it includes x and y and the x’s and y’s can be separated

Example

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Solution

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