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Popular >

derivative of ln(x-sqrt(x^2-1))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of sqrt(16-x^2)x

\int 16 - x^{2} x d x

integral from 0 to 3 of (3-x)^2

\int_{0}^{3} (3 - x)^{2} d x

y^{''}+5y^'+4y=8te^{2t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 t e^{2 t}

tangent of 2x^3+3x^2-180x-3 tangent of

2 x^{3} + 3 x^{2} - 180 x - 3

limit as x approaches+0+of \sqrt[3]{x}

x \to + 0 + lim (3 x)

Frequently Asked Questions (FAQ)

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