Differentiate f(x)=tan(x^3-1) with respect to x

Differentiate f(x)=tan(x^3-1) with respect to x.

Thanks a lot!

We need to use the chain rule:

Let u = x^3-1 then du/dx = 3x^2

y = tan(u) and dy/du = sec^2(u) = sec^2(x^3-1)

so dy/dx =dy/du*du/dx = sec^2(x^3-1)*3x^2= 3(x*sec(x^3-1))^2

Now that is fine for formal work but remember the tan function has a limited range (where -pi/2