What is (\partial)/(\partial x)(x+1/x) ?

The answer to (\partial)/(\partial x)(x+1/x) is 1-1/(x^2)

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(\partial)/(\partial x)(x+1/x)

\frac{\partial}{\partial x} (x + \frac{1}{x})

1 - \frac{1}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (x + \frac{1}{x})

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (\frac{1}{x})

\frac{\partial}{\partial x} (x) = 1

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

= 1 - \frac{1}{x ^{2}}

\frac{\partial}{\partial x} ((x - 1)^{2} \cdot (y + 4)^{2})

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 t}

f (x) = x 3 - 2 x^{2}

y^{^{'}} = - y, y (0) = 1

g (x) = \frac{2 x + 2}{x ^{2} + 2}

What is (\partial)/(\partial x)(x+1/x) ?
The answer to (\partial)/(\partial x)(x+1/x) is 1-1/(x^2)