How do you differentiate #f(x)=(5-x^2)(x^3-3x+3) # using the product rule?
1 Answer
Dec 27, 2015
Explanation:
Derivative of product rule
Given
#h' = fg' +f'g#
The original problem
#f'(x) = (5-x^2) d/dx(x^3-3x+3) + d/dx(5-x^2)(x^3-3x+3)#
#=> (5-x^2)(3x^2-3) + (-2x)(x^3-3x+3)#
Now we can multiply and combine like terms
#=> (15x^2 -15 -3x^4 +3x^2) +( -2x^4+6x^2 -6x)#
#=> -5x^4 +24x^2 -6x-15#