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

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

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

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

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

Solution steps

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

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

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

= 2 x + 0 - \frac{2}{y x ^{2}}

Simplify

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

r^{2} - 16 x^{2}

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

\frac{\partial}{\partial x} (r cos (x))

x \to 7 lim (3 x - 4)

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

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