derivative of (2-x/(sqrt(1-y)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{1}{4} sin (4 x) d x

s l o p e (- 3, 3), (4, - 5)

x \to - 4 lim ((x + 3)^{2})

\int \frac{x}{x ^{2} + x + 1} d x

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