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Popular >

derivative of ln|x^2-1|

Solution

\frac{d}{d x} (ln x^{2} - 1)

Solution

\frac{2 x}{x ^{2} - 1}

Solution steps

\frac{d}{d x} (ln x^{2} - 1)

Apply the chain rule:

\frac{1}{∣ x ^{2} - 1 ∣} \frac{d}{d x} (x^{2} - 1)

= \frac{1}{∣ x ^{2} - 1 ∣} \frac{d}{d x} (x^{2} - 1)

\frac{d}{d x} (x^{2} - 1) = \frac{2 x ( x ^{2} - 1 )}{∣ x ^{2} - 1 ∣}

= \frac{1}{∣ x ^{2} - 1 ∣} \cdot \frac{2 x ( x ^{2} - 1 )}{∣ x ^{2} - 1 ∣}

Simplify

\frac{1}{∣ x ^{2} - 1 ∣} \cdot \frac{2 x ( x ^{2} - 1 )}{∣ x ^{2} - 1 ∣} : \frac{2 x}{x ^{2} - 1}

= \frac{2 x}{x ^{2} - 1}

Popular Examples

integral of u/((u^2+1)(1-2u)(1+2u))

\int \frac{u}{( u ^{2} + 1 ) ( 1 - 2 u ) ( 1 + 2 u )} d u

integral of (7x+3)/(x^2-2x+1)

\int \frac{7 x + 3}{x ^{2} - 2 x + 1} d x

inverse oflaplace (e^{2s})/(s^3)inverse laplace

\frac{e ^{2 s}}{s ^{3}}

(\partial)/(\partial x)(xye^{sin(pixy)})

\frac{\partial}{\partial x} (x y e^{s i n (π x y)})

limit as x approaches-3 of (5-x) 4/3

x \to - 3 lim ((5 - x) \frac{4}{3})

Frequently Asked Questions (FAQ)

What is the derivative of ln|x^2-1| ?
The derivative of ln|x^2-1| is (2x)/(x^2-1)
What is the first derivative of ln|x^2-1| ?
The first derivative of ln|x^2-1| is (2x)/(x^2-1)