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Popular >

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

Solution

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

Solution

- \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}

Graph

Popular Examples

derivative of-6sin(2x)

\frac{d}{d x} (- 6 sin (2 x))

derivative of (sqrt(81+x^2)/3+(15-x)/5)

\frac{d}{d x} (\frac{81 + x ^{2}}{3} + \frac{15 - x}{5})

derivative of-sin(xy)

\frac{d}{d x} (- sin (x) y)

(\partial)/(\partial x)(-5ycos(-9x))

\frac{\partial}{\partial x} (- 5 y cos (- 9 x))

limit as x approaches infinity of 7-e^x

x \to \infty lim (7 - e^{x})

Frequently Asked Questions (FAQ)

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))