(\partial)/(\partial y)(ln(1+x^2+e^y+z))

Lösung

\frac{\partial}{\partial y} (ln (1 + x^{2} + e^{y} + z))

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

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (1 + x^{2} + e^{y} + z))

Behandle

x, z

als Konstanten

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{1 + x ^{2} + e ^{y} + z} e^{y} : \frac{e ^{y}}{1 + x ^{2} + e ^{y} + z}

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

in v erse l a pl a ce \frac{s ^{2} + 6 s + 2}{s ( s + 1 ) ^{2}}

y^{^{'}} = t y - 2 t + y - 2

l a pl a ce t r an s f or m 3 t^{3} - 2 t^{2} - 7 t + 2

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

d er i v a t i v e \frac{( x ^{2} + 11 )}{x ^{3}}