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

The derivative of (ln(x^2)^{-3}) is -3/(8xln^4(x))

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

The first derivative of (ln(x^2)^{-3}) is -3/(8xln^4(x))

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

- \frac{3}{8 x ln ^{4} ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{3}{ln ^{4} ( x ^{2} )} \cdot \frac{2}{x} : - \frac{3}{8 x ln ^{4} ( x )}

= - \frac{3}{8 x ln ^{4} ( x )}

\frac{d}{d x} (2 sin (π) x + 3 cos (π) x)

f (x) = \frac{7}{1 - x}

x \to 1.999 lim (2 x + 3)

\frac{d y}{d x} = (3 y + 6 x + 6 - 2)

\int sin (a + b x) d x

What is the derivative of (ln(x^2)^{-3}) ?
The derivative of (ln(x^2)^{-3}) is -3/(8xln^4(x))
What is the first derivative of (ln(x^2)^{-3}) ?
The first derivative of (ln(x^2)^{-3}) is -3/(8xln^4(x))