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Popular >

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

Solution

derivative of

y = 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

limit as x approaches 0+of ln(1/x)

x \to 0 + lim (ln (\frac{1}{x}))

limit as x approaches 1 of 7|x+1|-4

x \to 1 lim (7 ∣ x + 1 ∣ - 4)

derivative of y=(x-1)(x^2+x+1)derivative of

y = (x - 1) (x^{2} + x + 1)

(dy)/(dx)=(2x)/(y+1)

\frac{d y}{d x} = \frac{2 x}{y + 1}

integral from 1 to 1000 of (25)/(x^3)

\int_{1}^{1000} \frac{25}{x ^{3}} d x

Frequently Asked Questions (FAQ)

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