What is (\partial)/(\partial x)(ln(5x+2y)) ?

The answer to (\partial)/(\partial x)(ln(5x+2y)) is 5/(5x+2y)

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(\partial)/(\partial x)(ln(5x+2y))

\frac{\partial}{\partial x} (ln (5 x + 2 y))

\frac{5}{5 x + 2 y}

Solution steps

\frac{\partial}{\partial x} (ln (5 x + 2 y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{5 x + 2 y} \frac{\partial}{\partial x} (5 x + 2 y)

= \frac{1}{5 x + 2 y} \frac{\partial}{\partial x} (5 x + 2 y)

\frac{\partial}{\partial x} (5 x + 2 y) = 5

= \frac{1}{5 x + 2 y} \cdot 5

Simplify

\frac{1}{5 x + 2 y} \cdot 5 : \frac{5}{5 x + 2 y}

= \frac{5}{5 x + 2 y}

What is (\partial)/(\partial x)(ln(5x+2y)) ?
The answer to (\partial)/(\partial x)(ln(5x+2y)) is 5/(5x+2y)