Reglas de derivación

Si, $u=u(x),v=(x),w=(x)$ funciones de $x$ y a $a, b, c, n$ constantes, entonces
$\parbox{7cm}{ \begin{equation}\quad \frac{d}{dx}\,(c) = 0 \end... ...t(\sum_{i=1}^{n}u_{i}\right)= \sum_{i=1}^{n}\frac{du_{i}}{dx} \end{equation}}$ $\parbox{8cm}{ \begin{equation}\quad \frac{d}{dx}\,(cu)=c \frac{d... ...,\left(u^{p/q}\right) = \frac{p}{q}\,u^{p/q-1}\,\frac{du}{dx} \end{equation}}$

$$\quad \frac{d}{dx}(f\circ g)(x)=\frac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)$$ (1)

$$\quad \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}\qquad\qquad y=f(u) \quad u=g(x)$$ (2)

$$\quad \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dv}\cdot\frac{dv}{dx}\qquad\qquad y=f(u),\, u=g(v),\, v=g(x)$$ (3)

$$\quad \frac{dy}{dx}=\frac{1}{\dfrac{dx}{dy}}\$$ (4)

$$\quad \left\vert \begin{array}{cc} f_{11}(x) & f_{12}(x) \\ ... ... f_{11}(x) & f_{12}(x) \\ f'_{21}(x) & f'_{22}(x) \\ \end{array}\right\vert$$ (5)

        &vellip#vdots;

$$\quad \left\vert \begin{array}{ccc} f_{11}(x) & \cdots & f_{1n... ...\cdots & \cdots \\ f_{21}(x) & \cdots & f_{2n}(x) \\ \end{array}\right\vert$$ (6)