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

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

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

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

2 y x - y^{2}

Solution steps

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

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} (x y^{2})

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

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

= 2 y x - y^{2}

f (x) = 2 x + 3, (3, 3)

x \to \infty lim (arctan (8 x))

\int_{1}^{\infty} \frac{9}{x ^{4}} d x

\frac{\partial}{\partial x} ((x^{4} - 1) (x^{2} + 1))

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