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# Reglas de derivación ## Derivadas de funciones elementales | Función | Derivada | | :------ | :-------------------------- | | $y = k$ | $y' = 0$ | | $y = x$ | $y' = 1$ | | $y = x^n$ | $y' = nx^{n-1}$ | | $y = e^x$ | $y' = e^x...

# Reglas de derivación ## Derivadas de funciones elementales | Función | Derivada | | :------ | :-------------------------- | | $y = k$ | $y' = 0$ | | $y = x$ | $y' = 1$ | | $y = x^n$ | $y' = nx^{n-1}$ | | $y = e^x$ | $y' = e^x$ | | $y = a^x$ | $y' = a^x \cdot \ln a$ | | $y = \ln x$ | $y' = \frac{1}{x}$ | | $y = \log_a x$ | $y' = \frac{1}{x \ln a}$ | | $y = \sin x$ | $y' = \cos x$ | | $y = \cos x$ | $y' = -\sin x$ | | $y = \tan x$ | $y' = \frac{1}{\cos^2 x} = 1 + \tan^2 x$ | | $y = \cot x$ | $y' = -\frac{1}{\sin^2 x} = -(1 + \cot^2 x)$ | ## Reglas de derivación Sean $u = u(x)$ y $v = v(x)$ | Operación | Derivada | | :--------------- | :------------------------------- | | $y = k \cdot u$ | $y' = k \cdot u'$ | | $y = u \pm v$ | $y' = u' \pm v'$ | | $y = u \cdot v$ | $y' = u'v + uv'$ | | $y = \frac{u}{v}$ | $y' = \frac{u'v - uv'}{v^2}$ | | $y = u^n$ | $y' = nu^{n-1} \cdot u'$ | | $y = \sqrt{u}$ | $y' = \frac{u'}{2\sqrt{u}}$ | | $y = f(u)$ | $y' = f'(u) \cdot u'$ |