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Popular >

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

Solution

derivative of

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}

Popular Examples

(\partial)/(\partial x)(e^{x+y}(x^2-y^2))

\frac{\partial}{\partial x} (e^{x + y} (x^{2} - y^{2}))

integral from 0 to 1 of (x^2+sqrt(x))

\int_{0}^{1} (x^{2} + x) d x

integral from-1 to 2 of 3xsqrt(3x^2+2)

\int_{- 1}^{2} 3 x 3 x^{2} + 2 d x

\int 10 d x

limit as x approaches 2+of x

x \to 2 + lim (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))