Derivatives of Products and Quotients!!



    Product Rule!
If f(x) = r(x) . s(x) and if both derivatives exist, then
f '(x) = r(x) . s'(x) + s(x) . r'(x)
In words, this means the derivative of a product is the first function times the derivative of the second function plus the second function times the derivative of the first function!!


Sample problems.
               Solution:
f'(x) = 3x2(10x - 3) + 6x(5x2 - 3x)
     = 30x3 - 9x2 + 30x3 - 18x2
= 60x3 - 27x2





Sample problems



On to the chain rule!!