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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

x \to - 1 lim (\frac{3 x}{x ^{2} + 1})

\frac{\partial}{\partial x} (6 x y - 6 x)

x \to 7 lim (4 x)

\frac{d}{d x} (- x^{2} - 4 x + 4)

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