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

1 Answer
Jun 26, 2018

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