What is (\partial)/(\partial x)(ln(1/x)) ?

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

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(\partial)/(\partial x)(ln(1/x))

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

- \frac{1}{x}

Solution steps

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

Simplify

ln (\frac{1}{x}) : - ln (x)

= \frac{\partial}{\partial x} (- ln (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{\partial}{\partial x} (ln (x))

Apply the common derivative:

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

= - \frac{1}{x}

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

e^{5 t}

y^{^{'}} = - 2 y + 5

\frac{d}{d x} (\frac{e ^{x}}{2 x + 1})

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

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