Math — Implicit & Logarithmic Differentiation

\frac{d}{dx}[\ln y] = \frac{1}{y}\frac{dy}{dx}

y = x^x \Rightarrow \ln y = x\ln x

\frac{d}{dx}(xy) = y + x\frac{dy}{dx}

\text{differentiate both sides w.r.t. } x