en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(xsqrt(x^2-2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 x ^{2} - 2}{x ( x ^{2} - 2 )}

Popular Examples

y^{''}+2y^'+5y=2sin(2t)

y^{^{''}} + 2 y^{^{'}} + 5 y = 2 sin (2 t)

integral of tan^2(3x)sec^4(3x)

\int tan^{2} (3 x) sec^{4} (3 x) d x

integral of (csc^2(x)-1)cot(x)

\int (csc^{2} (x) - 1) cot (x) d x

derivative of 1/(6x-7)

\frac{d}{d x} (\frac{1}{6 x - 7})

limit as x approaches-1 of 3x^2-3x+3

x \to - 1 lim (3 x^{2} - 3 x + 3)

Frequently Asked Questions (FAQ)

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