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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y) = 0

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

= 0 - \frac{1}{x ^{2}}

Simplify

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

\int e^{- y x} d x

\frac{d}{d x} (\frac{6 x}{x - 1})

\int y e^{x} + sin (y) d x

\int_{0}^{2} 2 x^{2} x^{3} + 1 d x

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