What is (\partial)/(\partial x)(ln(3x+5y)) ?

The answer to (\partial)/(\partial x)(ln(3x+5y)) is 3/(3x+5y)

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(\partial)/(\partial x)(ln(3x+5y))

\frac{\partial}{\partial x} (ln (3 x + 5 y))

\frac{3}{3 x + 5 y}

Solution steps

\frac{\partial}{\partial x} (ln (3 x + 5 y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{3 x + 5 y} \frac{\partial}{\partial x} (3 x + 5 y)

= \frac{1}{3 x + 5 y} \frac{\partial}{\partial x} (3 x + 5 y)

\frac{\partial}{\partial x} (3 x + 5 y) = 3

= \frac{1}{3 x + 5 y} \cdot 3

Simplify

\frac{1}{3 x + 5 y} \cdot 3 : \frac{3}{3 x + 5 y}

= \frac{3}{3 x + 5 y}

What is (\partial)/(\partial x)(ln(3x+5y)) ?
The answer to (\partial)/(\partial x)(ln(3x+5y)) is 3/(3x+5y)