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

Lösung

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

\frac{x + 2}{2 ( x + 1 ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x x + 1) = \frac{3 x + 2}{2 x + 1}

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

= \frac{\frac{3 x + 2}{2 x + 1} ( x + 1 ) - 1 \cdot x x + 1}{( x + 1 ) ^{2}}

Vereinfache

\frac{\frac{3 x + 2}{2 x + 1} ( x + 1 ) - 1 \cdot x x + 1}{( x + 1 ) ^{2}} : \frac{x + 2}{2 ( x + 1 ) ^{\frac{3}{2}}}

= \frac{x + 2}{2 ( x + 1 ) ^{\frac{3}{2}}}

y^{^{'}} + 6 y = e^{t}

\int \frac{5}{3 - 2 cos ( x )} d x

\frac{\partial}{\partial x} (x cos (\frac{y}{z}))

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

\frac{\partial}{\partial y} (3 x^{2} y^{4})