What is (\partial)/(\partial x)(x^2y-1/(xy)) ?

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

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(\partial)/(\partial x)(x^2y-1/(xy))

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

2 x y + \frac{1}{x ^{2} y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= 2 x y + \frac{1}{x ^{2} y}

\frac{d}{d x} (arccot (x))

f (x) = x^{2} 9 - x^{2}

- \frac{1}{( 1 + t ) ^{2}}

6 y^{^{''}} - y^{^{'}} - y = 0

\frac{d}{d x} (5 x^{3} y^{4})

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