What is the derivative of ln(1/(sqrt(x))) ?

The derivative of ln(1/(sqrt(x))) is -1/(2x)

What is the first derivative of ln(1/(sqrt(x))) ?

The first derivative of ln(1/(sqrt(x))) is -1/(2x)

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

- \frac{1}{2 x}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{x} \frac{d}{d x} (x)

= \frac{1}{x} \frac{d}{d x} (x)

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

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

Simplify

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

= - \frac{1}{2 x}

x \to 2 lim ((5 x + 7)^{4})

\int \frac{x ^{3} + 1}{x + 2} d x

(e^{- x})^{^{'}}

x \to 0 - lim (e^{\frac{- 1}{x}})

\int \frac{2 x + 2}{( x ^{2} + 1 ) ( x - 1 ) ^{3}} d x

What is the derivative of ln(1/(sqrt(x))) ?
The derivative of ln(1/(sqrt(x))) is -1/(2x)
What is the first derivative of ln(1/(sqrt(x))) ?
The first derivative of ln(1/(sqrt(x))) is -1/(2x)