(\partial)/(\partial x)(ln((xy)/(y+z)))

Lösung

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

\frac{1}{x}

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (\frac{x y}{y + z}) = \frac{y}{y + z}

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

Vereinfache

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

= \frac{1}{x}

in v erse l a pl a ce \frac{6}{s ( s ^{2} + 2 s + 6 )}

t an g e n t f (x) = \frac{1 + x ^{2}}{x ^{2} - 1}

d er i v a t i v e y = ln (x + x^{2} - 6)

x \to 0 lim (ln (x^{2} + 1))

y^{^{''}} + 3 y^{^{'}} - 4 y = 0