The problem is as follows: Differentiate y = cos(a^3 + x^3)

my current solution:

By the chain rule

u = a^3 + x^3

f(u) = cos(u)

u' = 3a^2 + 3x^2 (by the power rule)

f ' (u) = -sin(u)

therefore,

-sin(a^3 + x^3)(3a^2 + 3x^2) = -3a^2sin(a^3 + x^3) - 3x^2sin(a^3 + x^3)

This is the solution I come up with, however it is incorrect and I don't know why.

correct solution should be -3x^2sin(a^3 + x^3). Where is the -3a^2sin(a^3 + x^3)

going?