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 )}

\int ln (x) d x

\int \frac{5 e ^{x}}{e ^{2 x} + 10 e ^{x} + 25} d x

x \to 2 lim (- (x))

y^{^{''}} = t

d y - (y - 4) 2 d x = 0

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))