Differentiate y= x^3 * tanx

To differentiate y = x^3
tanx.

The right side is a product of x^3 and tanx. So we
use  the product rule to differentiate:

(u(x)(v(x)}' =
u'(x)v(x) +u(x)v'(x).

Here u(x) = x^3 , u'(x) = (x^3)' =
3x^2

v(x) = tanx . (v(x))' = (tanx)' = 
sec^2x.

Therefore y' =
(x^3*tanx)'.

y'(x) = (x^3)'tanx
+x^3(tanx)'.

y' = 3x^2tanx+x^3*
sec^2x.

y' = x^2 {3tanx+xsec^2 x) .