(\partial)/(\partial y)(ln(e^x+e^y))

Lösung

\frac{\partial}{\partial y} (ln (e^{x} + e^{y}))

\frac{e ^{y}}{e ^{x} + e ^{y}}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (e^{x} + e^{y}))

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{e ^{x} + e ^{y}} \frac{\partial}{\partial y} (e^{x} + e^{y})

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

\frac{\partial}{\partial y} (e^{x} + e^{y}) = e^{y}

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

Vereinfache

\frac{1}{e ^{x} + e ^{y}} e^{y} : \frac{e ^{y}}{e ^{x} + e ^{y}}

= \frac{e ^{y}}{e ^{x} + e ^{y}}

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

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

\int \frac{1}{7 - 4 x - x ^{2}} d x

in v erse l a pl a ce \frac{( s + 1 )}{( s ^{2} + 2 s + 9 )}

a re a x = 3 y, x = 2 + y^{2}