Differentiation

Differentiation from First principles

$$f^{\text{'}}=\underset{h\to 0}{Lim}\left(\frac{f(x+h)-f\left(x\right)}{h}\right)$$ Basic diffs Constant factor Term wise

Chain rule

$$\frac{dy}{dx}=\frac{dy}{\mathrm{du}}\frac{\mathrm{du}}{\mathrm{dx}}$$

Product rule

$$\frac{\mathrm{d(uv)}}{\mathrm{dx}}=+$$

where $u$ and $v$ are functions of $x$

Quotient rule

$$f^{\text{'}}\left(\frac{u}{v}\right)=\frac{u^{\text{'}}v-u{v}^{\text{'}}}{v^2}$$

where $u$ and $v$ are functions of $x$

Parts