What is the derivative of 1/(x(ln(x)^{2/3)}) ?

The derivative of 1/(x(ln(x)^{2/3)}) is -(2+3ln(x))/(3x^2ln^{5/3)(x)}

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

The first derivative of 1/(x(ln(x)^{2/3)}) is -(2+3ln(x))/(3x^2ln^{5/3)(x)}

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

- \frac{2 + 3 ln ( x )}{3 x ^{2} ln ^{\frac{5}{3}} ( x )}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( x ln ^{\frac{2}{3}} ( x ) ) ^{2}} \cdot \frac{2 + 3 ln ( x )}{3 ln ^{\frac{1}{3}} ( x )} : - \frac{2 + 3 ln ( x )}{3 x ^{2} ln ^{\frac{5}{3}} ( x )}

= - \frac{2 + 3 ln ( x )}{3 x ^{2} ln ^{\frac{5}{3}} ( x )}

\frac{d}{d θ} (\frac{sin ( θ )}{1 + cos ( θ )})

\frac{\partial}{\partial z} (2 x z^{2} cos (y))

x \to 0 lim (\frac{x ^{2}}{x + 1})

\int sin^{3} (x) cos^{16} (x) d x

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

What is the derivative of 1/(x(ln(x)^{2/3)}) ?
The derivative of 1/(x(ln(x)^{2/3)}) is -(2+3ln(x))/(3x^2ln^{5/3)(x)}
What is the first derivative of 1/(x(ln(x)^{2/3)}) ?
The first derivative of 1/(x(ln(x)^{2/3)}) is -(2+3ln(x))/(3x^2ln^{5/3)(x)}