(\partial)/(\partial u)(sqrt(v/u))

Lösung

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

- \frac{v}{2 u ^{\frac{3}{2}}}

Schritte zur Lösung

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

Behandle

v

als Konstante

Wende die Kettenregel an:

\frac{1}{2 \frac{v}{u}} \frac{\partial}{\partial u} (\frac{v}{u})

= \frac{1}{2 \frac{v}{u}} \frac{\partial}{\partial u} (\frac{v}{u})

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

= \frac{1}{2 \frac{v}{u}} (- \frac{v}{u ^{2}})

Vereinfache

\frac{1}{2 \frac{v}{u}} (- \frac{v}{u ^{2}}) : - \frac{v}{2 u ^{\frac{3}{2}}}

= - \frac{v}{2 u ^{\frac{3}{2}}}

\frac{d}{d x} (ln (\frac{9 - x}{5 + x}))

d er i v a t i v e - 9 x^{2}

\frac{d}{d x} (arccos (cos (x)))

im pl i c i t \frac{d y}{d x}, x y = x - 2 y

\frac{d y}{d x} = \frac{( x - 3 )}{y - 4}