Techniques of Differentiation - Differentiation by First Principles

Let \(y = x^n\), where \(n\) is an integer. Using the first principles, or otherwise, prove that \(\frac{\mathrm{d}y}{\mathrm{d}x} = nx^{n-1}\).

For negative \(n\), exclude \(x=0\). For \(n=0\), the function is constant and its derivative is zero; do not interpret the formal product \(0x^{-1}\) at zero.