What is (\partial)/(\partial x)(x^2+y/x) ?

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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