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

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

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

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

\frac{1}{x + 4 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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