(\partial)/(\partial v)(tan(u/v))

Lösung

\frac{\partial}{\partial v} (tan (\frac{u}{v}))

- \frac{u sec ^{2} ( \frac{u}{v} )}{v ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial v} (tan (\frac{u}{v}))

Behandle

u

als Konstante

Wende die Kettenregel an:

sec^{2} (\frac{u}{v}) \frac{\partial}{\partial v} (\frac{u}{v})

= sec^{2} (\frac{u}{v}) \frac{\partial}{\partial v} (\frac{u}{v})

\frac{\partial}{\partial v} (\frac{u}{v}) = - \frac{u}{v ^{2}}

= sec^{2} (\frac{u}{v}) (- \frac{u}{v ^{2}})

Vereinfache

sec^{2} (\frac{u}{v}) (- \frac{u}{v ^{2}}) : - \frac{u sec ^{2} ( \frac{u}{v} )}{v ^{2}}

= - \frac{u sec ^{2} ( \frac{u}{v} )}{v ^{2}}

n = 3 \sum \infty \frac{2}{n ( n + 2 )}

\int - 5 csc^{2} (x) d x

x \to - 3 + lim (\frac{x + 4}{x + 3})

x \to + (- 4) lim (∣ x + 4 ∣)

3 x \frac{d y}{d x} + y = x