(\partial)/(\partial y)(ln(y/x))

Lösung

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

\frac{1}{y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{\frac{y}{x}} \cdot \frac{1}{x}

Vereinfache

\frac{1}{\frac{y}{x}} \cdot \frac{1}{x} : \frac{1}{y}

= \frac{1}{y}

x \to - 2 lim (4 - 3 x^{2})

x \to 0 + lim (3 + x^{8} ln (x))

\int - \frac{20}{y ^{21}} d y

t an g e n t f (x) = x^{2} - x^{4}, at x = 1

\frac{\partial}{\partial x} (9 x^{3 y})