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

The derivative of sqrt(x^2+1/(x^2)) is (x^4-1)/(x^2sqrt(x^4+1))

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

The first derivative of sqrt(x^2+1/(x^2)) is (x^4-1)/(x^2sqrt(x^4+1))

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Popular >

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

\frac{x ^{4} - 1}{x ^{2} x ^{4} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x ^{2} + \frac{1}{x ^{2}}} (2 x - \frac{2}{x ^{3}}) : \frac{x ^{4} - 1}{x ^{2} x ^{4} + 1}

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

n = 0 \sum \infty \frac{7 ^{n}}{6 ^{n}}

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What is the derivative of sqrt(x^2+1/(x^2)) ?
The derivative of sqrt(x^2+1/(x^2)) is (x^4-1)/(x^2sqrt(x^4+1))
What is the first derivative of sqrt(x^2+1/(x^2)) ?
The first derivative of sqrt(x^2+1/(x^2)) is (x^4-1)/(x^2sqrt(x^4+1))