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)

Popular >

derivative of

(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}}

\frac{\partial}{\partial x} (\frac{1}{( x ^{2} + y ^{2} )})

(x^{4} + y^{4}) d x - (x y^{3}) d y = 0

\int \frac{1}{( x ^{2} + 25 ) ^{2}} d x

f (x) = (\frac{9}{8}) x^{\frac{8}{9}}

\frac{\partial}{\partial y} (4 - x^{2} - 2 y^{2})

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)