If we let u = 2x³ - 1 then y = u⁴.

So now

• y is written as a power of u; and
• u is a function of x [ u = f(x) ].

To find the derivative of such an expression, we can use our new rule:

`d/(dx)u^n=n u^(n-1)(du)/(dx`

where u = 2x³ − 1 and n = 4.

So

` {: ((dy)/(dx),=n u^(n-1)(du)/(dx)),(,=[4(2x^3-1)^3][6x^2]),(,=24x^2(2x^3-1)^3) :}`

We could, of course, use the chain rule, as before:

`(dy)/(dx)=(dy)/(du)(du)/(dx`