(\partial)/(\partial y)(tan(x/y))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (- \frac{x}{5 y})

x \to 0 lim (- \frac{1}{x ^{3}})

s im pl i f y sin (2 t)

x \to + 3 lim (4 cos (x))

\int x ln (\frac{1 - x}{1 + x}) d x