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

The answer to (\partial)/(\partial x)(ln(2/x)) is -1/x

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

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

- \frac{1}{x}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{\frac{2}{x}} (- \frac{2}{x ^{2}})

Simplify

\frac{1}{\frac{2}{x}} (- \frac{2}{x ^{2}}) : - \frac{1}{x}

= - \frac{1}{x}

x^{2} y^{^{''}} + x y^{^{'}} - y = 2 x

- \frac{6}{x ^{7}}

\int \frac{1}{( x - 1 ) ( x - 3 )} d x

\frac{d}{d x} (sin (\frac{3}{x}))

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

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