Lista de derivadas de funciones elementales

f\left(x\right) = a
f'\left(x\right) = 0
f\left(x\right) = xf'\left(x\right) = 1
f\left(x\right) = axf'\left(x\right) = a
f\left(x\right) = ax + bf'\left(x\right) = a
f\left(x\right) = x^nf'\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^xf'\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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