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Popular >

derivative of |ln|x||

Solution

\frac{d}{d x} (∣ ln ∣ x ∣ ∣)

Solution

\frac{ln ∣ x ∣}{x ∣ ln ∣ x ∣ ∣}

Solution steps

\frac{d}{d x} (∣ ln ∣ x ∣ ∣)

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{ln ∣ x ∣}{x ∣ ln ∣ x ∣ ∣}

Graph

Popular Examples

derivative of 5/2

\frac{d}{d x} (\frac{5}{2})

(\partial)/(\partial x)(8xln(xy-7))

\frac{\partial}{\partial x} (8 x ln (x y - 7))

derivative of 4arccos(-5x)

\frac{d}{d x} (4 arccos (- 5 x))

area 1,\sqrt[4]{x},0,1 area

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d/(dθ)(2cos(θ)+4sin(θ))

\frac{d}{d θ} (2 cos (θ) + 4 sin (θ))

Frequently Asked Questions (FAQ)

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