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Popular >

derivative of ln(ln(12x))

Solution

\frac{d}{d x} (ln (ln (12 x)))

Solution

\frac{1}{x ln ( 12 x )}

Solution steps

\frac{d}{d x} (ln (ln (12 x)))

Apply the chain rule:

\frac{1}{ln ( 12 x )} \frac{d}{d x} (ln (12 x))

= \frac{1}{ln ( 12 x )} \frac{d}{d x} (ln (12 x))

\frac{d}{d x} (ln (12 x)) = \frac{1}{x}

= \frac{1}{ln ( 12 x )} \cdot \frac{1}{x}

Simplify

\frac{1}{ln ( 12 x )} \cdot \frac{1}{x} : \frac{1}{x ln ( 12 x )}

= \frac{1}{x ln ( 12 x )}

Popular Examples

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\int \frac{1}{2 sin ^{2} ( x ) + 3 cos ^{2} ( x )} d x

y^{''}+81y=cos(2t)

y^{^{''}} + 81 y = cos (2 t)

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(\partial)/(\partial z)(xsin(y-z))

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Frequently Asked Questions (FAQ)

What is the derivative of ln(ln(12x)) ?
The derivative of ln(ln(12x)) is 1/(xln(12x))
What is the first derivative of ln(ln(12x)) ?
The first derivative of ln(ln(12x)) is 1/(xln(12x))