Question

I need to find dy/dx of 3cos^2 2x - 3sin^2 2x

Answer 1

d/dx cos²(x³) ..................... use the chain rule 3 times as follows
= d/dz cos²(z) dz/dx ......... z = x³
= d/du u² du/dz dz/dx ...... u = cos(z)
= (2u) (-sin(z)) (3x²) ......... du/dz = -sin(z) , d/du u² = 2u, dz/dx = 3x²
= -6x² cos(x³) sin(x³)

Answer: -6x² cos(x³) sin(x³)