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Popular Calculus >

derivative of ln(x+sqrt(x^2-12))

Solution

\frac{d}{d x} (ln (x + x^{2} - 12))

Solution

\frac{1}{x ^{2} - 12}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 12))

Apply the chain rule:

\frac{1}{x + x ^{2} - 12} \frac{d}{d x} (x + x^{2} - 12)

= \frac{1}{x + x ^{2} - 12} \frac{d}{d x} (x + x^{2} - 12)

\frac{d}{d x} (x + x^{2} - 12) = 1 + \frac{x}{x ^{2} - 12}

= \frac{1}{x + x ^{2} - 12} (1 + \frac{x}{x ^{2} - 12})

Simplify

\frac{1}{x + x ^{2} - 12} (1 + \frac{x}{x ^{2} - 12}) : \frac{1}{x ^{2} - 12}

= \frac{1}{x ^{2} - 12}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x+sqrt(x^2-12)) ?
The derivative of ln(x+sqrt(x^2-12)) is 1/(sqrt(x^2-12))
What is the first derivative of ln(x+sqrt(x^2-12)) ?
The first derivative of ln(x+sqrt(x^2-12)) is 1/(sqrt(x^2-12))