Question

Find f'(x) for f(x) = cos^2(3x^3).

Answer 1

`f(x) = \cos^2(3x^3)\\f'(x) = (d)/(dx)[\cos^2(3x^3)]\\= 2\cos(3x^3) \cdot (d)/(dx)[cos(3x^3)]\\= 2\cos(3x^3) \cdot (-\sin(3x^3)) \cdot (d)/(dx)[3x^3]\\= 2\cos(3x^3) \cdot (-\sin(3x^3)) \cdot 9x^2\\= -18x^2\cos(3x^3)\sin(3x^3)`