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Popular >

derivative of ln|ln(10x)|

Solution

derivative of

ln ∣ ln (10 x) ∣

Solution

\frac{1}{x ln ( 10 x )}

Solution steps

\frac{d}{d x} (ln ∣ ln (10 x) ∣)

Apply the chain rule:

\frac{1}{∣ ln ( 10 x ) ∣} \frac{d}{d x} (∣ ln (10 x) ∣)

= \frac{1}{∣ ln ( 10 x ) ∣} \frac{d}{d x} (∣ ln (10 x) ∣)

\frac{d}{d x} (∣ ln (10 x) ∣) = \frac{ln ( 10 x )}{x ∣ ln ( 10 x ) ∣}

= \frac{1}{∣ ln ( 10 x ) ∣} \cdot \frac{ln ( 10 x )}{x ∣ ln ( 10 x ) ∣}

Simplify

\frac{1}{∣ ln ( 10 x ) ∣} \cdot \frac{ln ( 10 x )}{x ∣ ln ( 10 x ) ∣} : \frac{1}{x ln ( 10 x )}

= \frac{1}{x ln ( 10 x )}

Popular Examples

derivative of x(x-10^2)

\frac{d}{d x} (x (x - 10)^{2})

integral of 1/(x*ln(x^9))

\int \frac{1}{x \cdot ln ( x ^{9} )} d x

y^'+2xy=x*e^{-x^2}

y^{^{'}} + 2 x y = x \cdot e^{- x^{2}}

(\partial)/(\partial x)(2ln((x+y)^3))

\frac{\partial}{\partial x} (2 ln ((x + y)^{3}))

derivative of (14x-x^2^3)

\frac{d}{d x} ((14 x - x^{2})^{3})

Frequently Asked Questions (FAQ)

What is the derivative of ln|ln(10x)| ?
The derivative of ln|ln(10x)| is 1/(xln(10x))
What is the first derivative of ln|ln(10x)| ?
The first derivative of ln|ln(10x)| is 1/(xln(10x))