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martes, 25 de marzo de 2014

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]

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