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Popular >

derivative of 1/((ln(x)^3))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= - \frac{3}{( ln ( x ) ) ^{4}} \cdot \frac{1}{x}

Simplify

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

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

Popular Examples

integral of (x^2+3)/(x+1)

\int \frac{x ^{2} + 3}{x + 1} d x

integral of 1/(sqrt(3-8x-x^2))

\int \frac{1}{3 - 8 x - x ^{2}} d x

limit as x approaches 1 of (x-11)/(x+7)

x \to 1 lim (\frac{x - 11}{x + 7})

integral of 1/(usqrt(6-u^2))

\int \frac{1}{u 6 - u ^{2}} d u

derivative of (x^4/4+1/(8x^2))

\frac{d}{d x} (\frac{x ^{4}}{4} + \frac{1}{8 x ^{2}})

Frequently Asked Questions (FAQ)

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