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Popular >

derivative of ln(x+sqrt(x^2-2))

Solution

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

Solution

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

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

Simplify

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

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

Popular Examples

integral of 3sin^3(x)cos^2(x)

\int 3 sin^{3} (x) cos^{2} (x) d x

integral of 2cos^3(t)

\int 2 cos^{3} (t) d t

t y^{^{'}} - 3 y = t^{4}

integral of x/(sqrt(3-x^2))

\int \frac{x}{3 - x ^{2}} d x

integral of (x^2-2x+6)/((x+1)(x-2)^2)

\int \frac{x ^{2} - 2 x + 6}{( x + 1 ) ( x - 2 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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