Standard derivatives

The idea

Bring the power down and reduce it by one: $\frac{d}{dx}(x^n) = nx^{n-1}$. Also $\frac{d}{dx}(e^{kx}) = ke^{kx}$, $\frac{d}{dx}(\ln x) = \frac{1}{x}$, $\frac{d}{dx}(\sin kx) = k\cos kx$ and $\frac{d}{dx}(\cos kx) = -k\sin kx$, with $x$ in radians.

1. Rewrite roots and fractions as powers: $\sqrt{x} = x^{\frac{1}{2}}$, $\frac{2}{x} = 2x^{-1}$.
2. Differentiate term by term.
3. Constants differentiate to $0$.

Watch out Rewrite $\frac{4}{x^2}$ as $4x^{-2}$ before you differentiate.