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Popular >

derivative of ln(x+sqrt(x^2+a^2))

Solution

derivative of

ln (x + x^{2} + a^{2})

Solution

\frac{1}{x ^{2} + a ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x ^{2} + a ^{2}}

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Frequently Asked Questions (FAQ)

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