What is (\partial)/(\partial y)(ln(x+2y+3z)) ?

The answer to (\partial)/(\partial y)(ln(x+2y+3z)) is 2/(x+2y+3z)

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(\partial)/(\partial y)(ln(x+2y+3z))

\frac{\partial}{\partial y} (ln (x + 2 y + 3 z))

\frac{2}{x + 2 y + 3 z}

Solution steps

\frac{\partial}{\partial y} (ln (x + 2 y + 3 z))

Treat

x, z

as constants

Apply the chain rule:

\frac{1}{x + 2 y + 3 z} \frac{\partial}{\partial y} (x + 2 y + 3 z)

= \frac{1}{x + 2 y + 3 z} \frac{\partial}{\partial y} (x + 2 y + 3 z)

\frac{\partial}{\partial y} (x + 2 y + 3 z) = 2

= \frac{1}{x + 2 y + 3 z} \cdot 2

Simplify

\frac{1}{x + 2 y + 3 z} \cdot 2 : \frac{2}{x + 2 y + 3 z}

= \frac{2}{x + 2 y + 3 z}

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What is (\partial)/(\partial y)(ln(x+2y+3z)) ?
The answer to (\partial)/(\partial y)(ln(x+2y+3z)) is 2/(x+2y+3z)