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

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

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

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

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derivative of

\frac{1}{x + \frac{1}{x}}

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to + (- 0) lim (f (x))

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

\int_{1}^{16} \frac{x - 7}{x} d x

\int \frac{4}{( 1 + 2 x ) ^{3}} d x

\int_{1}^{e^{5}} \frac{ln ^{3} ( x ^{2} )}{x} d x

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