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)^{'} |
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