derivative of (sqrt(x+1)/x)

Lösung

\frac{d}{d x} (\frac{x + 1}{x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 1}{x})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 9 y^{3}))

\frac{d y}{d x} = 2 - 3 y

\int_{0}^{1} \frac{2}{( x + 2 ) ^{2}} d x

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

\int \frac{- 2}{5 x ^{2}} d x