derivative of ln(y/x)

Lösung

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

\frac{x \frac{d y}{d x} - y}{x y}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

= \frac{x \frac{d y}{d x} - y}{x y}

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

d er i v a t i v e \frac{x ^{2}}{( x ^{2} - 1 ) ^{4}}

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

s l o p e in t erce pt (7) (- 1.6)

x^{2} y^{^{'}} + 2 x y = 11 cos^{2} (x)