What is (\partial)/(\partial x)(ln(2x+4y+9z)) ?

The answer to (\partial)/(\partial x)(ln(2x+4y+9z)) is 2/(2x+4y+9z)

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(\partial)/(\partial x)(ln(2x+4y+9z))

\frac{\partial}{\partial x} (ln (2 x + 4 y + 9 z))

\frac{2}{2 x + 4 y + 9 z}

Solution steps

\frac{\partial}{\partial x} (ln (2 x + 4 y + 9 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{2 x + 4 y + 9 z} \frac{\partial}{\partial x} (2 x + 4 y + 9 z)

= \frac{1}{2 x + 4 y + 9 z} \frac{\partial}{\partial x} (2 x + 4 y + 9 z)

\frac{\partial}{\partial x} (2 x + 4 y + 9 z) = 2

= \frac{1}{2 x + 4 y + 9 z} \cdot 2

Simplify

\frac{1}{2 x + 4 y + 9 z} \cdot 2 : \frac{2}{2 x + 4 y + 9 z}

= \frac{2}{2 x + 4 y + 9 z}

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What is (\partial)/(\partial x)(ln(2x+4y+9z)) ?
The answer to (\partial)/(\partial x)(ln(2x+4y+9z)) is 2/(2x+4y+9z)