derivative of x/y+y/x

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\int_{2}^{4} (x^{2} + 2)^{3} d x

y^{^{''}} + y = t, y (0) = 1, y (1) = - 2

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{8 x ^{\frac{7}{8}}})

l a pl a ce t r an s f or m e^{- 2 t} (2 cos (3 t) - sin (3 t))

x \to \infty lim (\frac{5}{x})