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)

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

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}}

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)