What is (\partial)/(\partial x)(x^2+y^2+(32)/(xy)) ?

The answer to (\partial)/(\partial x)(x^2+y^2+(32)/(xy)) is 2x-(32)/(x^2y)

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(\partial)/(\partial x)(x^2+y^2+(32)/(xy))

\frac{\partial}{\partial x} (x^{2} + y^{2} + \frac{32}{x y})

2 x - \frac{32}{x ^{2} y}

Solution steps

\frac{\partial}{\partial x} (x^{2} + y^{2} + \frac{32}{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{32}{x y})

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

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

\frac{\partial}{\partial x} (\frac{32}{x y}) = - \frac{32}{y x ^{2}}

= 2 x + 0 - \frac{32}{y x ^{2}}

Simplify

= 2 x - \frac{32}{x ^{2} y}

\frac{d}{d x} (sec^{2} (2 x) 2)

x \to 1 lim (e^{(x \cdot 3 - x)})

x \to 1 - lim (x - 1)

\int cosh^{2} (x - 1) sinh (x - 1) d x

What is (\partial)/(\partial x)(x^2+y^2+(32)/(xy)) ?
The answer to (\partial)/(\partial x)(x^2+y^2+(32)/(xy)) is 2x-(32)/(x^2y)