What is the derivative of sqrt(1+1/(x^2)) ?

The derivative of sqrt(1+1/(x^2)) is -1/(x^2sqrt(x^2+1))

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

The first derivative of sqrt(1+1/(x^2)) is -1/(x^2sqrt(x^2+1))

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

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

Solution steps

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

Apply the chain rule:

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

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

Simplify

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

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

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