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Popular Calculus >

derivative of ln(x+sqrt(x^2-5))

Solution

\frac{d}{d x} (ln (x + x^{2} - 5))

Solution

\frac{1}{x ^{2} - 5}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 5))

Apply the chain rule:

\frac{1}{x + x ^{2} - 5} \frac{d}{d x} (x + x^{2} - 5)

= \frac{1}{x + x ^{2} - 5} \frac{d}{d x} (x + x^{2} - 5)

\frac{d}{d x} (x + x^{2} - 5) = 1 + \frac{x}{x ^{2} - 5}

= \frac{1}{x + x ^{2} - 5} (1 + \frac{x}{x ^{2} - 5})

Simplify

\frac{1}{x + x ^{2} - 5} (1 + \frac{x}{x ^{2} - 5}) : \frac{1}{x ^{2} - 5}

= \frac{1}{x ^{2} - 5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(x^2-5)) ?
The derivative of ln(x+sqrt(x^2-5)) is 1/(sqrt(x^2-5))
What is the first derivative of ln(x+sqrt(x^2-5)) ?
The first derivative of ln(x+sqrt(x^2-5)) is 1/(sqrt(x^2-5))