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# CRMS Calculus 2010 January 13, 2010

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Calculus rule for differentiating the product of two functions.

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### CRMS Calculus 2010 January 13, 2010

1. 1. Do you remember ? The curve of forgetting Rules of Differentiation 1
2. 2. Exploration 4­2: Derivative of a Product of Two Function Objective: Given a function that is a product of two other functions, find in one step an equation for the derivative  function. Does differentiation distribute over addition                         No?       or       Yes? Let u be a function of x. u = x3 Let v be a function of x. v = 5x + 1 Let y =  u  +  v y = ___________________ Therefore: = ? = + 2
3. 3. Does differentiation distribute over multiplication                               No?       or       Yes? Let u be a function of x. u = x3 Let v be a function of x. v = 5x + 1 . Let y =  u     v             y = ___________________ Therefore: = ? = . Time for a new derivative technique ! 3
4. 4. http://www.calculus­help.com/funstuff/tutorials/derivatives/deriv03.html Derivative of the first times the second, plus the first times the derivative of the second. 4
5. 5. 1. If y = x4 cos 6x, find y'. 2. If f(x) = (3x­8)7(4x+9)5, find f'(x). 5
6. 6. 3.  If y = esinx, find y''. 4.  If y = x­6.3 ln4x, find y’. 6
7. 7. 5. If y = 3x5(x2 ­ 4)cos 10x, find y’.  (Be clever!) 7
8. 8. 8