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

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

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

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

\frac{2}{2 x + y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{1}{x}

x^{2} - 18 x + 1

\frac{6 s ^{2} + 8}{s ( s ^{2} + 4 )}

\frac{d y}{d x}, y^{2} cos (\frac{1}{y}) = 2 x + 2 y

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