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Popular >

derivative of y=ln(6(ln(x))^8)

Solution

derivative of

y = ln (6 (ln (x))^{8})

Solution

\frac{8}{x ln ( x )}

Solution steps

\frac{d}{d x} (ln (6 (ln (x))^{8}))

Apply the chain rule:

\frac{1}{6 ( ln ( x ) ) ^{8}} \frac{d}{d x} (6 (ln (x))^{8})

= \frac{1}{6 ( ln ( x ) ) ^{8}} \frac{d}{d x} (6 (ln (x))^{8})

\frac{d}{d x} (6 (ln (x))^{8}) = \frac{48 ln ^{7} ( x )}{x}

= \frac{1}{6 ( ln ( x ) ) ^{8}} \cdot \frac{48 ln ^{7} ( x )}{x}

Simplify

\frac{1}{6 ln ^{8} ( x )} \cdot \frac{48 ln ^{7} ( x )}{x} : \frac{8}{x ln ( x )}

= \frac{8}{x ln ( x )}

Popular Examples

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x \to 8 - lim (x - 8)

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x \to 0 lim (\frac{2 cos ( x ) - 2}{x})

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x \to \infty lim (7^{x})

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(6(ln(x))^8) ?
The derivative of y=ln(6(ln(x))^8) is 8/(xln(x))
What is the first derivative of y=ln(6(ln(x))^8) ?
The first derivative of y=ln(6(ln(x))^8) is 8/(xln(x))