Differentiation

The derivative

$\frac{dy}{dx}$ gives the gradient. Power rule: $$\frac{d}{dx}(x^n)=nx^{n-1}$$ Differentiate term by term; constants → 0. Rewrite roots/fractions as powers first (e.g. $\frac{1}{x^2}=x^{-2}$, $\sqrt x = x^{1/2}$).