Question

How do you differentiate `f(x)=(2x^3)(cos^2x^2)` using the product rule?

Answer 1

`2x^3*2*cosx^2*-sin(x)^2*2x+cos^2x^2*6x^2`

Explanation:

we have
`f(x)=(2x^3)(cos^2x^2)`
`dy/dx=2x^3*d(cos^2x^2)/dx+(cos^2x^2)*d(2x^3)/dx`

`=>2x^3*2*d(cosx^2)/dx+(cos^2x^2)*2*3*x^2`.....using`[dy/dx=x^n=>nx^(n-1)]`
`=>2x^3*2*(cosx^2)*-sind(x^2)/dx+(cos^2x^2)*6*x^2`
.........using `[dy/dx=cosx=>-sinx]`
`=>2x^3*2*(cosx^2)*-sinx^2*2x+(cos^2x^2)*6*x^2`