How do you differentiate #g(x) = (5x^6 - 4)(x^2-4)# using the product rule?
1 Answer
Feb 25, 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)=5x^6-4rArrf'(x)=30x^5#
#"and "h(x)=x^2-4rArrh'(x)=2x#
#rArrg'(x)=(5x^6-4).(2x)+(x^2-4).(30x^5)#
#color(white)(rArrg'(x))=10x^7-8x+30x^7-120x^5#
#color(white)(rArrg'(x))=40x^7-120x^5-8x#
