derivative of (-y^2/((x-y)^2))

Lösung

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

- \frac{2 y ( x \frac{d y}{d x} - y )}{( x - y ) ^{3}}

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Streiche

\frac{2 y \frac{d y}{d x} ( x - y ) ^{2} - 2 ( x - y ) ( 1 - \frac{d y}{d x} ) y ^{2}}{( ( x - y ) ^{2} ) ^{2}} : \frac{2 y ( x \frac{d y}{d x} - y )}{( x - y ) ^{3}}

= - \frac{2 y ( x \frac{d y}{d x} - y )}{( x - y ) ^{3}}

\frac{\partial ^{2}}{\partial x ^{2}} (sin^{2} (m x + n y))

in v erse l a pl a ce \frac{1}{( s - 1 ) ^{5}}

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

\int \frac{2}{( x - 2 ) ^{2}} d x

a re a x = y^{2} - 8, x = 8