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Popular >

derivative of (1+1/x ^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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\int (- x)^{2 n} d x

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f (x) = 2 t^{- \frac{3}{4}}

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derivative of (3x^2-5x-2/(4x+12))

\frac{d}{d x} (\frac{3 x ^{2} - 5 x - 2}{4 x + 12})

(\partial)/(\partial y)(x^3-3x+y-e^y)

\frac{\partial}{\partial y} (x^{3} - 3 x + y - e^{y})

Frequently Asked Questions (FAQ)

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