To find the [[derivative]] of a function raised to a power, bring down the exponent as a coefficient and decrement the exponent by 1. Discard any constants. For a function $f(x) = x^n$ the power rule states that the derivative is $f'(x) = nx^{n-1}$ To demonstrate, let's find the derivative of the function $f(x) = x^2$ using the definition of the derivative. First we can find $f(x + h)$ $f(x + h) = (x + h)^2 = x^2 + 2xh + h^2$ Then we use the definition of the derivative $f'(x) = \lim_{h \to 0} \frac{(x^2 + 2xh + h^2) - x^2}{h}$ Which simplifies to $f'(x) = \lim_{h \to 0} \frac{2xh + h^2}{h} = \lim_{h \to 0} 2x + h$ We can substitute $0$ in for $h$ since we are taking the limit and reduce to $f'(x) = 2x$