(\partial)/(\partial y)(ln(x/y))

Lösung

\frac{\partial}{\partial y} (ln (\frac{x}{y}))

- \frac{1}{y}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (\frac{x}{y}))

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{1}{y}

x \to 0 lim (\frac{2}{x} - \frac{2}{x})

a re a \frac{2}{x}, \frac{2}{x ^{2}}, x = 4

d er i v a t i v e f (x) = 6 sec (x) - 5 x

\frac{d}{d x} (sec (5) x^{2})

n = 1 \sum \infty \frac{7}{n ^{5}}