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

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

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

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

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

- \frac{1}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{x}

y^{^{'}} = 0.0875 - \frac{7 y}{2000}, y (0) = 50

f (x) = \frac{( 3 x + 5 )}{1 + x}, at x = 1

\frac{d}{d x} (3 x^{2} - 6 x - 8)

\int \frac{e ^{x}}{x - 1} d x

x \to 0 lim (ln (1 - 5 x))

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