What is the derivative of f(x) = 3(x^3)* cosx

f(x) = 3x^3 * cosx

First we
will treat the funtion as a produt of two functions of
x.

Let us assume that:

f(x) =
u(x) *v(x)  such tht:

u(x)= 3x^3     ===>     u'(x)
= 9x^2

v(x) = cosx    ===>       v'(x) = -
sinx

Now we know that th product rule
is:

f'(x) = u'(x) *v(x) +
u(x)*v'(x)

        = 9x^2 *cosx + 3x^3 *
-sinx

          = (9x^2)cosx -
(3x^3)sinx

==> f'(x) = (9x^2)cosx -
(3x^3)*sinx