# How do you use the product rule to differentiate #g(x)=(x^2+1)(x^2-2x)#?

##### 1 Answer

Jan 14, 2017

#### Explanation:

#"Given " g(x)=f(x).h(x)" then"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(g'(x)=f(x)h'(x)+h(x)f'(x))color(white)(2/2)|)))larr" product rule"#

#"here " f(x)=x^2+1rArrf'(x)=2x#

#"and " h(x)=x^2-2xrArrh'(x)=2x-2#

#rArrg'(x)=(x^2+1)(2x-2)+(x^2-2x).2x#

#=2x^3-2x^2+2x-2+2x^3-4x^2#

#=4x^3-6x^2+2x-2#