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

The derivative of 1/(x(ln(x)^3)) is -(ln(x)+3)/(x^2ln^4(x))

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

The first derivative of 1/(x(ln(x)^3)) is -(ln(x)+3)/(x^2ln^4(x))

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

- \frac{ln ( x ) + 3}{x ^{2} ln ^{4} ( x )}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( x ln ^{3} ( x ) ) ^{2}} (ln^{3} (x) + 3 ln^{2} (x)) : - \frac{ln ( x ) + 3}{x ^{2} ln ^{4} ( x )}

= - \frac{ln ( x ) + 3}{x ^{2} ln ^{4} ( x )}

x \to 2 lim (- (x))

d er i v a t i v e f (x) = 4 + 8 x - 5 x^{2}

\frac{d y}{d x} = 3 (y + 7) x^{2}

d er i v a t i v e \frac{1 - 3 t}{6 + t}

x \to 0 lim (- sin (x))

What is the derivative of 1/(x(ln(x)^3)) ?
The derivative of 1/(x(ln(x)^3)) is -(ln(x)+3)/(x^2ln^4(x))
What is the first derivative of 1/(x(ln(x)^3)) ?
The first derivative of 1/(x(ln(x)^3)) is -(ln(x)+3)/(x^2ln^4(x))