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Popular >

derivative of ln(1+1/(x^2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + \frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

= \frac{1}{1 + \frac{1}{x ^{2}}} (- \frac{2}{x ^{3}})

Simplify

\frac{1}{1 + \frac{1}{x ^{2}}} (- \frac{2}{x ^{3}}) : - \frac{2}{x ( x ^{2} + 1 )}

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

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f (1) = \frac{8}{x} - x x

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\int 4 x^{2} + 7 d x

(\partial)/(\partial x)(4x^2sqrt(y^3-xz))

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sum from n=1 to infinity of (1+n)/(3^n)

n = 1 \sum \infty \frac{1 + n}{3 ^{n}}

integral of 8sin^2(x)

\int 8 sin^{2} (x) d x

Frequently Asked Questions (FAQ)

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