(\partial)/(\partial x)(sqrt(y/x))

Lösung

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

- \frac{y}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 \frac{y}{x}} \frac{\partial}{\partial x} (\frac{y}{x})

= \frac{1}{2 \frac{y}{x}} \frac{\partial}{\partial x} (\frac{y}{x})

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

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

Vereinfache

\frac{1}{2 \frac{y}{x}} (- \frac{y}{x ^{2}}) : - \frac{y}{2 x ^{\frac{3}{2}}}

= - \frac{y}{2 x ^{\frac{3}{2}}}

\int_{0}^{x} t^{2} + t^{4} d t

\frac{d y}{d x} = y^{2} - 4

\frac{\partial}{\partial x} (sin (5 π x + 2 y))

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

d er i v a t i v e \frac{1}{2 r} + \frac{1}{6 r ^{\frac{5}{6}}}