(\partial)/(\partial y)(ln(x+y/(2x)))

Lösung

\frac{\partial}{\partial y} (ln (x + \frac{y}{2 x}))

\frac{1}{2 x ^{2} + y}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (x + \frac{y}{2 x}))

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{x + \frac{y}{2 x}} \cdot \frac{1}{2 x}

Vereinfache

\frac{1}{x + \frac{y}{2 x}} \cdot \frac{1}{2 x} : \frac{1}{2 x ^{2} + y}

= \frac{1}{2 x ^{2} + y}

y^{^{'}} = - 10 y

\int_{0}^{\infty} e^{a x} d x

\frac{\partial}{\partial y} (x ln (5 x + 8 y))

\frac{d}{d t} (0. 9^{t})

x \to 0 lim (\frac{x - 9}{x - 1})