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Popular >

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

Solution

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

Solution

- \frac{1}{2 x ^{\frac{3}{2}} x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt((x+1/x)) ?
The derivative of sqrt((x+1/x)) is -1/(2x^{3/2)sqrt(x+1)}
What is the first derivative of sqrt((x+1/x)) ?
The first derivative of sqrt((x+1/x)) is -1/(2x^{3/2)sqrt(x+1)}