(\partial)/(\partial x)(x/(x^2+xy+y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Quotientenregel an:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 9

a re a 5, x^{2} + 1

\int \frac{x ^{6} - x ^{4} + x ^{2}}{x ^{3}} d x

\int_{\frac{1}{2}}^{1} (x^{- 3} - 10) d x

\frac{d}{d x} (5 sin (x) + 6 cos (x))