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

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

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

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

y^{2} - 2 y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= y^{2} - 2 y x

y = 4 - x^{2}, y = - 3 x

\int_{1}^{2} π (\frac{1}{x})^{2} d x

\int_{5}^{11} \frac{16}{x - 1} d x

\int_{0}^{1} (x^{2} - x)^{2} d x

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

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