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Popular >

derivative of ln|ln(x|)

Solution

\frac{d}{d x} (ln ∣ ln (x) ∣)

Solution

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

Solution steps

\frac{d}{d x} (ln ∣ ln (x) ∣)

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of y=x^{(1/(ln(x)))}derivative of

y = x^{(\frac{1}{l n ( x )})}

integral of sin^5(x)*cos^5(x)

\int sin^{5} (x) \cdot cos^{5} (x) d x

limit as x approaches 0 of 7/(cos(x))

x \to 0 lim (\frac{7}{cos ( x )})

(dx)/(dy)+1/(y^2)x= 1/(y^2)

\frac{d x}{d y} + \frac{1}{y ^{2}} x = \frac{1}{y ^{2}}

derivative of f(x)=x^2(4x^3-1)derivative of

f (x) = x^{2} (4 x^{3} - 1)

Frequently Asked Questions (FAQ)

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