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

Lösung

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

\frac{1}{y ^{2}} + \frac{2 y}{x ^{3}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

= \frac{1}{y ^{2}} + \frac{2 y}{x ^{3}}

d er i v a t i v e (x^{2})^{- 1}

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

\int \frac{1}{x ( 10 - x )} d x

\frac{\partial}{\partial x} (\frac{x + 2}{y + 1})

\frac{d}{d x} (x e^{9 x})