P(x) = (x - 3cosx)(x + 3cosx) = x^2 - 9cos^2(x)
dp/dx = 2x - 9d(cos^2x) = 2x - 9*2cosx*d(cosx) =
= 2x - 9*2cosx(- sinx) =
2x + 9*2sinxcosx =
2x + 9sin(2x)
you can use the formula
(a - b)(a + b) = a^2 - b^2
2sinxcosx = sin(2x)
or you can use the product rule
dp/dx = (d( x - 3cosx))(x + 3cosx) + ( x - 3cosx)(d(x + 3cosx)) =
(1 + 3sinx)(x + 3cosx) + ( x - 3cosx)(1 - 3sinx) =
x + 3cosx + 3xsinx + 9 sinxcosx + x -3cosx - 3xsinx + 9 sinxcosx =
2x + 18 sinxcosx = 2x + 9*2sinxcosx= 2x + 9 sin(2x)