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

The derivative of 1/(sqrt(ln(x))) is -1/(2xln^{3/2)(x)}

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

The first derivative of 1/(sqrt(ln(x))) is -1/(2xln^{3/2)(x)}

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

- \frac{1}{2 x ln ^{\frac{3}{2}} ( x )}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

= - \frac{1}{2 ( ln ( x ) ) ^{\frac{3}{2}}} \frac{d}{d x} (ln (x))

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

= - \frac{1}{2 ( ln ( x ) ) ^{\frac{3}{2}}} \cdot \frac{1}{x}

Simplify

- \frac{1}{2 ln ^{\frac{3}{2}} ( x )} \cdot \frac{1}{x} : - \frac{1}{2 x ln ^{\frac{3}{2}} ( x )}

= - \frac{1}{2 x ln ^{\frac{3}{2}} ( x )}

n = 1 \sum \infty 3 (\frac{7}{2})^{n - 1}

x \to 0 + lim (tan (3 x))

\frac{d}{d x} (0.5 x^{3})

\int \frac{x}{2 x - 5} d x

What is the derivative of 1/(sqrt(ln(x))) ?
The derivative of 1/(sqrt(ln(x))) is -1/(2xln^{3/2)(x)}
What is the first derivative of 1/(sqrt(ln(x))) ?
The first derivative of 1/(sqrt(ln(x))) is -1/(2xln^{3/2)(x)}