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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

limit as t approaches x/2 of (sin(t))/t

t \to \frac{x}{2} lim (\frac{sin ( t )}{t})

slope of (-3.5)(4.3)slope

(- 3.5) (4.3)

(\partial)/(\partial x)(-x/(y^2))

\frac{\partial}{\partial x} (- \frac{x}{y ^{2}})

inverse oflaplace (s+2)/(s^2+2s+2)inverse laplace

\frac{s + 2}{s ^{2} + 2 s + 2}

limit as x approaches-4 of 7-x

x \to - 4 lim (7 - 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)