derivative of sqrt(y/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{2 \frac{y}{x}} \cdot \frac{x \frac{d y}{d x} - y}{x ^{2}}

Vereinfache

\frac{1}{2 \frac{y}{x}} \cdot \frac{x \frac{d y}{d x} - y}{x ^{2}} : \frac{x \frac{d y}{d x} - y}{2 x ^{\frac{3}{2}} y}

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

\frac{d}{d x} (arcsin (\frac{a x}{4}))

\frac{\partial}{\partial y} (- 5 e^{x} cos (yz))

\int \frac{a}{2} x + \frac{a}{2} d x

x \to 8 lim (2 x - 7 x^{2})

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