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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

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

d er i v a t i v e y = \frac{7 x - 3}{5 x + 4} + x^{3}

\int 8 e^{2 x} d x

\frac{d}{d x} ((x^{2} + 5)^{3})

\frac{d}{d t} (3 e^{2 t})