What is (\partial)/(\partial y)(ln(x+y+z)) ?

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{5 e ^{- s}}{s + 1}

\int_{0}^{3} π (x)^{2} d x

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\int \frac{1}{X} d X

\int \frac{2 x}{e ^{x^{2}}} d x

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