Derivative of cos x

The derivative of cos x, [cos x]',
is -sin x.

y = cos (x³ - 4) is a composite function of
y = cos (whole) and (whole) = x³ - 4.

So the derivative of the composite function is,
the derivative of the outer function cos (x³ - 4), -sin (x³ - 4)
times,
the derivative of the inner function x³ - 4, 3x².

Arrange the expression.

So -3x² sin (x³ - 4) is the derivative of cos (x³ - 4).