How do you differentiate #f(x)=(2x^2+1)(3x-3)# using the product rule?
1 Answer
Dec 31, 2015
Explanation:
The product rule states that for some function
#f(x)=g(x)h(x),f'(x)=g'(x)h(x)+h'(x)g(x)#
Here, we have
#{(g(x)=2x^2+1),(h(x)=3x-3):}#
Differentiate each function.
#{(g'(x)=4x),(h'(x)=3):}#
Relate these to find
#f'(x)=4x(3x-3)+3(2x^2+1)#
Distribute and simplify.
#f'(x)=18x^2-12x+3#