Question

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

Answer 1

`f'(x)=(3x^2+6x)cosx+(6x+6)sinx`

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`