Question

How do you find the derivative of `y=6 cos(x^3+3)` ?

Answer 1

This is a composite of the function `x^3+3` and the function `6cos x`, so we will need the Chain Rule together with `(x^3+3)=3x^2` and `(cos x)'=-sin x` (as shown here:derivative of trig functions ).

Thus
`(6cos(x^3+3))'=-6sin(x^3+3)\times (x^3+3)'=-18x^2 sin(x^3+3)`.