derivative (1+sqrt(X))/(1-sqrt(X))

Lösung

ableitung von

\frac{1 + X}{1 - X}

\frac{1}{X ( 1 - X ) ^{2}}

Schritte zur Lösung

\frac{d}{d X} (\frac{1 + X}{1 - X})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{1}{X ( 1 - X ) ^{2}}

\int e^{c o s (25 t)} sin (25 t) d t

t an g e n t x + \frac{5}{x}

\frac{x d y}{d x} - y = x^{2017} \cdot y^{2}

\frac{\partial}{\partial x} ((2 - x y) e^{- x y})

\frac{\partial}{\partial x} ((2 x + 2 y) e^{y})