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Popular >

derivative of (x+1/x ^2)

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (2) = 0

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

= 2 x + 0 - \frac{2}{x ^{3}}

Simplify

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

Popular Examples

d/(dt)((t-2)^2)

\frac{d}{d t} ((t - 2)^{2})

(\partial)/(\partial x)(yx+y)

\frac{\partial}{\partial x} (y x + y)

integral from 6 to 3 of (9x^2-4x+9)

\int_{6}^{3} (9 x^{2} - 4 x + 9) d x

integral of (-x-3)/(x^3-x)

\int \frac{- x - 3}{x ^{3} - x} d x

integral of (2x+3)/(x(x+1)(x-1))

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

Frequently Asked Questions (FAQ)

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