TABLA DE DERIVADAS E INTEGRALES

$$ \begin{array}{lll} \textbf{Función} & \textbf{Derivada} & \textbf{Integral} \\ \\ y = c & 0 & cx \\ y = c x & c & c \cdot \dfrac{x^2}{2} \\ y = x^n & n x^{n-1} & \dfrac{x^{n+1}}{n+1} \\ y = \dfrac{1}{x} & \dfrac{-1}{x^2} & \ln{x} \\ y = \sqrt{x} & \dfrac{1}{2\sqrt{x}} & \dfrac{2x^{3/2}}{3} \\ y = x^{\frac{a}{b}} & \dfrac{a x^{\frac{a}{b}-1}}{b} & \dfrac{x^{\frac{a}{b}+1}}{\frac{a}{b}+1} \\ y = \ln{x} & \dfrac{1}{x} & x \ln{x} - x \\ y = \log_a{x} & \dfrac{1}{x \ln a} & x \log_a x - \dfrac{x}{\ln a} \\ y = e^x & e^x & e^x \\ y = a^x & a^x \ln a & \dfrac{a^x}{\ln a} \\ y = x^x & x^x (\ln x + 1) & — \\ y = \sin x & \cos x & -\cos x \\ y = \cos x & -\sin x & \sin x \\ y = \tan x & \sec^2 x & -\ln|\cos x| \\ y = \cot x & -\csc^2 x & \ln|\sin x| \\ y = \sec x & \sec x \tan x & \ln|\sec x + \tan x| \\ y = \csc x & -\csc x \cot x & \ln|\csc x - \cot x| \\ y = \sin^{-1} x & \dfrac{1}{\sqrt{1-x^2}} & x \sin^{-1} x + \sqrt{1-x^2} \\ y = \cos^{-1} x & \dfrac{-1}{\sqrt{1-x^2}} & x \cos^{-1} x - \sqrt{1-x^2} \\ y = \tan^{-1} x & \dfrac{1}{1+x^2} & x \tan^{-1} x - \dfrac{1}{2}\ln(1+x^2) \\ y = \sec^{-1} x & \dfrac{1}{x \sqrt{x^2 - 1}} & — \\ y = \sinh x & \cosh x & \cosh x \\ y = \cosh x & \sinh x & \sinh x \\ y = \tanh x & \operatorname{sech}^2 x & \ln \cosh x \\ y = \coth x & -\operatorname{csch}^2 x & \ln \sinh x \\ y = \dfrac{1}{\cosh x} & -\dfrac{\tanh x}{\cosh x} & — \\ y = \dfrac{1}{\sinh x} & -\dfrac{\coth x}{\sinh x} & — \\ y = u \cdot v & u'v + uv' & \int u \, dv = uv - \int v \, du \\ y = \dfrac{u}{v} & \dfrac{u'v - uv'}{v^2} & — \\ y = e^u & e^u \cdot u' & — \\ \end{array} $$