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

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

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

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

\frac{2}{x ( x + 2 )}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{\frac{x}{x + 2}} \cdot \frac{2}{( x + 2 ) ^{2}}

Simplify

\frac{1}{\frac{x}{x + 2}} \cdot \frac{2}{( x + 2 ) ^{2}} : \frac{2}{x ( x + 2 )}

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

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