# How do you differentiate #f(x)=3x*(x+2)*sinx # using the product rule?

##### 1 Answer

Feb 3, 2017

#### Answer:

#### 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#