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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{2}{ln ( x )}

x \to 2 lim (\frac{x ^{2} + 2}{x - 2})

\int_{0}^{2} - 2 x 4 - x^{2} d x

d er i v a t i v e 13 x e^{x}

x \to 0 lim (14 x + 7 h)