derivative of (x^2+2/x)

解答

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

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

求解步骤

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

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= \frac{2 xx - 1 \cdot ( x ^{2} + 2 )}{x ^{2}}

化简

\frac{2 xx - 1 \cdot ( x ^{2} + 2 )}{x ^{2}} : \frac{x ^{2} - 2}{x ^{2}}

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

\int \frac{- 5 e ^{- 5 x}}{( e ^{- 5 x} + 3 ) ^{3}} d x

s \to 2 - lim (s + ∣ 3 s - 6 ∣)

\frac{d}{d x} (\frac{sin ( x ) + cos ( x )}{sin ( x )})

j o in \frac{a x ^{2}}{ln ( \frac{x}{4} )} + \frac{b x ^{4}}{x - 4}

\frac{\partial}{\partial x} (3 x^{2} y^{2} - 1)