How can we find the gradient for any tangent line to a function \(y=x^n\), where \(n\) is a positive integer?

In Quadratic and cubic we were given a power of \(x\), \(f(x)=x^2\) or \(x^3\), and we took the point \((3,f(3))\) and another point \((3+h,f(3+h))\) and found the gradient of the line through these two points for \(h\) a very small number.

If we did this here, what would be the gradient of the line through \((3,f(3))\) and \((3+h,f(3+h))\), for smaller and smaller values of \(h\)?

How can we generalise this for any point on the curve \(y=x^n\)?