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Popular >

derivative of (ln(x)^{-1})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=x^{4/3}derivative of

y = x^{\frac{4}{3}}

inverse oflaplace 1/(s^2-1)inverse laplace

\frac{1}{s ^{2} - 1}

integral from 0 to pi of cos(x)sin(x)

\int_{0}^{π} cos (x) sin (x) d x

integral from 0 to pi/6 of 64sin^2(x)

\int_{0}^{\frac{π}{6}} 64 sin^{2} (x) d x

integral of (cos(pi/(x^{31)}))/(x^{32)}

\int \frac{cos ( \frac{π}{x ^{31}} )}{x ^{32}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (ln(x)^{-1}) ?
The derivative of (ln(x)^{-1}) is -1/(xln^2(x))
What is the first derivative of (ln(x)^{-1}) ?
The first derivative of (ln(x)^{-1}) is -1/(xln^2(x))