# Lista de derivadas de funciones elementales

 $f\left(x\right) = a$ $f'\left(x\right) = 0$ $f\left(x\right) = x$ $f'\left(x\right) = 1$ $f\left(x\right) = ax$ $f'\left(x\right) = a$ $f\left(x\right) = ax + b$ $f'\left(x\right) = a$ $f\left(x\right) = x^n$ $f'\left(x\right) = nx^{n-1}$ $f\left(x\right) = \sqrt{x}$ $f'\left(x\right) = \frac{1}{2\sqrt{x}}$ $f\left(x\right) = e^x$ $f'\left(x\right) = e^x$ $f\left(x\right) = \ln(x)$ $f'\left(x\right) = \frac{1}{x}$ $f\left(x\right) = a^x (a >0)$ $f'\left(x\right) = a^x \ln(a)$ $f\left(x\right) = \log_{b}(x)$ $f'\left(x\right) = \frac{1}{x\ln(b)}$ $f\left(x\right) = \frac{1}{x^n} = (x^n)^{-1} = x^{-n}$ $f'\left(x\right) = -nx^{-n-1} = -nx^{-(n+1)} = \frac{-n}{x^{n+1}}$ $f\left(x\right) = \operatorname{sen}(x)$ $f'\left(x\right) = \cos(x)$ $f\left(x\right) = \cos(x)$ $f'\left(x\right) = -\operatorname{sen}(x)$ $f\left(x\right) = \tan(x)$ $f'\left(x\right)=\sec^2(x)=\frac{1}{cos^2(x)}=1+\tan^2(x)$ $f\left(x\right) = \csc(x)$ $f'\left(x\right) = -\csc(x)\cot(x)$ $f\left(x\right) = \sec(x)$ $f'\left(x\right) = \sec(x)\tan(x)$ $f\left(x\right) = \cot(x)$ $f'\left(x\right) = -\csc^2(x)$ $f\left(x\right) = \operatorname{arcsen}(x)$ $f'\left(x\right) = \frac{1}{\sqrt{1-x^2}}$ $f\left(x\right) = \arccos(x)$ $f'\left(x\right) = \frac{-1}{\sqrt{1-x^2}}$ $f\left(x\right) = \arctan(x)$ $f'\left(x\right) = \frac{1}{1+x^2}$ $f\left(x\right) = g(x) \pm h(x)$ $f'\left(x\right) = g'(x) \pm h'(x)$ $f\left(x\right) = g(x) \cdot h(x)$ $f'\left(x\right) = g'(x) \cdot h(x) + g(x) \cdot h'(x)$ $f\left(x\right) = \frac{g(x)}{h(x)}$ $f'\left(x\right) = \frac{g'(x) \cdot h(x) - g(x) \cdot h'(x)}{h^2(x)}$ $f\left(x\right) = k \cdot g(x)$ $f'\left(x\right) = k \cdot g'(x)$ $f\left(x\right) = g \circ h = g(h(x))$ $f'\left(x\right) = (g'\circ h) \cdot h' = g'(h(x)) \cdot h'(x)$
Lista de derivadas de funciones elementales
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