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Popular >

derivative of ln((sqrt(4+x^2)/x))

Solution

\frac{d}{d x} (ln (\frac{4 + x ^{2}}{x}))

Solution

- \frac{4}{x ( x ^{2} + 4 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 + x ^{2}}{x}))

Apply the chain rule:

\frac{1}{\frac{4 + x ^{2}}{x}} \frac{d}{d x} (\frac{4 + x ^{2}}{x})

= \frac{1}{\frac{4 + x ^{2}}{x}} \frac{d}{d x} (\frac{4 + x ^{2}}{x})

\frac{d}{d x} (\frac{4 + x ^{2}}{x}) = - \frac{4}{x ^{2} 4 + x ^{2}}

= \frac{1}{\frac{4 + x ^{2}}{x}} (- \frac{4}{x ^{2} 4 + x ^{2}})

Simplify

\frac{1}{\frac{4 + x ^{2}}{x}} (- \frac{4}{x ^{2} 4 + x ^{2}}) : - \frac{4}{x ( x ^{2} + 4 )}

= - \frac{4}{x ( x ^{2} + 4 )}

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Frequently Asked Questions (FAQ)

What is the derivative of ln((sqrt(4+x^2)/x)) ?
The derivative of ln((sqrt(4+x^2)/x)) is -4/(x(x^2+4))
What is the first derivative of ln((sqrt(4+x^2)/x)) ?
The first derivative of ln((sqrt(4+x^2)/x)) is -4/(x(x^2+4))