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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x, y

als Konstanten

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce s + 3

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\int (2 cos (x) + 4 sin (x) + 6) d x

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