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Derivatives

Derivatives. By Mendy Kahan & Jared Friedman. What is a Derivative?. Let ’ s say we were given some function called “ f ” and the derivative of that function is “ f` ” . f` represents the slope of the tangent line to the graph at point x. This is represented by:.

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Derivatives

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  1. Derivatives By Mendy Kahan & Jared Friedman

  2. What is a Derivative? Let’s say we were given some function called “f” and the derivative of that function is “f`”. f` represents the slope of the tangent line to the graph at point x. This is represented by:

  3. How Do We Take Derivatives?

  4. Chain Rule This rule should be used for difficult problems involving composite functions This can also be written as: The derivative of this composition is given by the formula:

  5. For more Examples: http://web.mit.edu/wwmath/calculus/differentiation/chain.html http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/derivative/chain.html http://www.exambot.com/cgi/topic/show.cgi/math/difc/diff/dcha Chain Rule Examples

  6. Product Rule

  7. Product Rule Examples For more Examples: http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/productruledirectory/ProductRule.html

  8. Quotient Rule =

  9. Quotient Rule Examples For more Examples: http://www.math.hmc.edu/calculus/tutorials/quotient_rule/

  10. High Order Derivatives The rules for taking higher order derivatives are basically identical to taking a regular derivative. Once you take the first derivative of the answer repeat this process as many times as necessary to find the nth derivative. However, there are sometimes patterns and it would be very time consuming to take higher order derivatives. Ex: For more examples: http://www.exambot.com/cgi/topic/show.cgi/math/difc/diff/hder

  11. Higher Order Derivative Ex: • Find the 7th derivative • The pattern repeats every 4th derivative so: • Find the pattern of the derivatives of sin x Since the remainder is 3, the 7th derivative of sin x is the same as the 3rd derivative.

  12. Derivatives of Trigonometric Functions

  13. Trigonometric Function Example For more examples: http://www.sosmath.com/calculus/diff/der03/der03.html

  14. Derivatives of Exponential Logarithmic Functions Rules: Ex: For more examples: http://www.exambot.com/cgi/problem/show.cgi/math/difc/diff/dcha/1166.pr?a

  15. The End • Now you are ready to take the test!!!

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