What is (\partial}{\partial x}(ln(\frac{x-2)/3)) ?

The answer to (\partial}{\partial x}(ln(\frac{x-2)/3)) is 1/(x-2)

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(\partial}{\partial x}(ln(\frac{x-2)/3))

\frac{\partial}{\partial x} (ln (\frac{x - 2}{3}))

\frac{1}{x - 2}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{x - 2}{3}))

Apply the chain rule:

\frac{1}{\frac{x - 2}{3}} \frac{\partial}{\partial x} (\frac{x - 2}{3})

= \frac{1}{\frac{x - 2}{3}} \frac{\partial}{\partial x} (\frac{x - 2}{3})

\frac{\partial}{\partial x} (\frac{x - 2}{3}) = \frac{1}{3}

= \frac{1}{\frac{x - 2}{3}} \cdot \frac{1}{3}

Simplify

\frac{1}{\frac{x - 2}{3}} \cdot \frac{1}{3} : \frac{1}{x - 2}

= \frac{1}{x - 2}

What is (\partial}{\partial x}(ln(\frac{x-2)/3)) ?
The answer to (\partial}{\partial x}(ln(\frac{x-2)/3)) is 1/(x-2)