derivative of (x+y/(xy))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

y^{^{'}} = 1 - \frac{y}{20}

7 x^{2} y^{^{'}} = y^{^{'}} + 9 x e - y

\int_{1}^{\infty} \frac{1}{x ^{2} + x} d x

\frac{d}{d x} (2^{x} ln^{2} (2))

a re a 9 x + 11, 7 x + 14, [23, 13]