How do you differentiate #f(x)=3x*(x+2)*sinx # using the product rule?
1 Answer
Feb 3, 2017
Explanation:
#"Given "f(x)=g(x)h(x)" then"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))larr" product rule"# We can express f(x) as the product of 2 functions.
#rArrf(x)=(3x^2+6x)sinx#
#"here "g(x)=3x^2+6xrArrg'(x)=6x+6#
#"and "h(x)=sinxrArrh'(x)=cosx#
#rArrf'(x)=(3x^2+6x)cosx+(6x+6)sinx#