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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

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

\int \frac{81 - x ^{2}}{x ^{2}} d x

x \to - 1 lim (x)

d er i v a t i v e f (x) = \frac{5 x ^{\frac{3}{2}} - 1 5 ^{\frac{1}{2}}}{2}

\int_{- 5}^{5} 25 - x^{2} d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) \cdot (x + 5 x^{3}))