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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

in v erse l a pl a ce \frac{1}{s + 1} \cdot \frac{1}{s}

n = 0 \sum \infty n (\frac{1}{4})^{n}

x \to 0 lim (- 6 + 6 x^{3})

y = 3^{2} + 3

\int e^{2 a x} d x