derivative of arctan(x-x^2)

解答

\frac{d}{d x} (arctan (x) - x^{2})

\frac{1}{x ^{2} + 1} - 2 x

求解步骤

\frac{d}{d x} (arctan (x) - x^{2})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (arctan (x)) - \frac{d}{d x} (x^{2})

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

\frac{d}{d x} (x^{2}) = 2 x

= \frac{1}{x ^{2} + 1} - 2 x

\int sin (7 x) ln (sin (7 x)) d x

y^{^{'}} = 2 (1 + y^{2}) x

\frac{d}{d x} (2 x - 1 - \frac{1}{x})

\int \frac{1}{( 1 - x ^{2} ) ^{\frac{1}{2}}} d x

\frac{\partial}{\partial x} (e^{- \frac{x}{y}} + ln (\frac{y}{x}))