What is (\partial)/(\partial x)(ln(x+8y+4z)) ?

The answer to (\partial)/(\partial x)(ln(x+8y+4z)) is 1/(x+8y+4z)

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(\partial)/(\partial x)(ln(x+8y+4z))

\frac{\partial}{\partial x} (ln (x + 8 y + 4 z))

\frac{1}{x + 8 y + 4 z}

Solution steps

\frac{\partial}{\partial x} (ln (x + 8 y + 4 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x + 8 y + 4 z} \frac{\partial}{\partial x} (x + 8 y + 4 z)

= \frac{1}{x + 8 y + 4 z} \frac{\partial}{\partial x} (x + 8 y + 4 z)

\frac{\partial}{\partial x} (x + 8 y + 4 z) = 1

= \frac{1}{x + 8 y + 4 z} \cdot 1

Simplify

= \frac{1}{x + 8 y + 4 z}

What is (\partial)/(\partial x)(ln(x+8y+4z)) ?
The answer to (\partial)/(\partial x)(ln(x+8y+4z)) is 1/(x+8y+4z)