微分の公式集

\left\{f(x)g(x)\right\}^{\prime} = f^{\prime}(x)g(x) + f(x)g^{\prime}(x)

\left\{\frac{f(x)}{g(x)}\right\}^{\prime} = \frac{f^{\prime}(x)g(x) - f(x)g^{\prime}(x)}{\left\{g(x)\right\}^2}

\frac{d}{dx} x^n = n x^{n-1}

\frac{d}{dx} e^x = e^x

\frac{d}{dx} e^{ax} = ae^{ax}

\frac{d}{dx} a^x = a^x \ln{a}

\frac{d}{dx} \sin{x} = \cos{x}

\frac{d}{dx} \cos{x} = -\sin{x}

\frac{d}{dx} \tan{x} = \frac{1}{\cos^2{x}}

\frac{d}{dx} \sinh{x} = \cosh{x}

\frac{d}{dx} \cosh{x} = \sinh{x}

\frac{d}{dx} \ln{x} = \frac{1}{x}

\frac{d}{dx} \log_a{x} = \frac{1}{x \ln{a}}

\frac{d}{dx} \arcsin{x} = \frac{1}{\sqrt{1-x^2}}

\frac{d}{dx} \arccos{x} = -\frac{1}{\sqrt{1-x^2}}

\frac{d}{dx} \arctan{x} = \frac{1}{1+x^2}