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

The answer to (\partial)/(\partial z)(ln(1+x^2+e^y+z)) is 1/(1+x^2+e^y+z)

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

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

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

Solution steps

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

Treat

x, y

as constants

Apply the chain rule:

\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

Simplify

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

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

s + 3

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What is (\partial)/(\partial z)(ln(1+x^2+e^y+z)) ?
The answer to (\partial)/(\partial z)(ln(1+x^2+e^y+z)) is 1/(1+x^2+e^y+z)