Resumen de las reglas de derivación

$f(x)$ $f^{'}(x)$ $c \;\; \text{(constant)}$ $0$ $x^k \quad , k \in \mathbb{R} \; \text{, constant)}$ $k\cdot x^{k-1}$ $c\cdot u(x)$ $c\cdot u^{'}(x)$ $u(x)+v(x)$ $u^{'}(x)+v^{'}(x)$ $(u \circ v )(x)$ $u_{v}^{'}\cdot(v^{'}(x)$ $\sin{\big(u(x)\big)}$ $\cos{\big(u(x)\big)}\cdot u^{'}(x)$ $\tan(u(x))$ $\displaystyle \dfrac{1}{\cos^{2}\big(x\big)}\cdot u^{'}(x)$ $e^{u(x)}$ $e^{u(x)}\cdot u^{'}(x)$ $\ln{u(x)}$ $\displaystyle \dfrac{1}{u(x)}\cdot u^{'}(x)$ $u(x) \cdot v(x)$ $u^{'}(x)\cdot v(x) + v^{'}(x)\cdot u(x)$ $\displaystyle \dfrac{u(x)}{v(x)}$ $\displaystyle \dfrac{u^{'}(x)\cdot v(x) - v^{'}(x)\cdot u(x)}{\big(v(x)\big)^2}$ $\big(u(x)\big)^{v(x)}$ $ \displaystyle\big(u(x)\big)^{v(x)}\cdot \Big(\dfrac{u^{'}(x)}{u(x)}\cdot v(x) + v^{'}(x) \cdot \ln{\big(u(x)\big)} \Big)$ $\arcsin{\big(u(x)\big)}$ $ \displaystyle \dfrac{1}{\sqrt{1-\big(u(x)\big)^2}}\cdot \big(u(x)\big)^{'}$ $\arccos{\big(u(x)\big)}$ $ \displaystyle -\dfrac{1}{\sqrt{1-\big(u(x)\big)^2}}\cdot \big(u(x)\big)^{'}$ $\arctan{\big(u(x)\big)}$ $ \displaystyle \dfrac{1}{1+\big(u(x)\big)^2}\cdot \big(u(x)\big)^{'}$

[nota del autor]