What the "steps" are depends on what methods you have learned. Part way through a Calculus course you probably would have learned the "power rule",
dxdxn=nxn−1, and that
dxdaf(x)=adxdf. If you know that then you know that
dxdaxn=naxn−1.
If you do not know those then you will need to use the basic definition of the derivative:
dxdf=h→0limhf(x+h)−f(x).
With
f(x)=axn then
f(x+h)=a(x+h)n. That's why Subhotash Kahn asked "Can you expand: (x + h)^n)?".
You can use the "binomial expansion":
(x+h)n=∑(ni)xihn−i where
(ni) is the "binomial coefficient"
i!(n−i)n!.
That can be expanded as
xn+nxn−1h+2n(n−1)xn−2h2+⋅⋅⋅. Then
f(x+h)−f(x)=xn+nxn−1h+2n(n−1)xn−2h2+⋅⋅⋅−xn=nxn−1h+2n(n−1)xn−2h2+⋅⋅⋅.
Notice the "h" in the first term,
h2 in the next term, and higher powers of h in succeeding terms. When we divide by h we get
nxn−1+2n(n−1)xn−2h2+⋅⋅⋅ where there is no h in the first term but powers of h in every term after that. Taking the limit as h goes to 0, all terms except the first term goes to 0.
The limit, as h goes to 0, is
nxn−1.