Calculus rule for differentiating the product of two functions.

1. Do you remember ?
The curve of forgetting
Rules of Differentiation
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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. 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 !
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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.
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5. 1. If y = x4 cos 6x, find y'.
2. If f(x) = (3x­8)7(4x+9)5, find f'(x).
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6. 3. If y = esinx, find y''.
4. If y = x­6.3 ln4x, find y’.
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7. 5. If y = 3x5(x2 ­ 4)cos 10x, find y’. (Be clever!)
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