What is (\partial)/(\partial x)(xy^2-x^3y) ?

The answer to (\partial)/(\partial x)(xy^2-x^3y) is y^2-3yx^2

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(\partial)/(\partial x)(xy^2-x^3y)

\frac{\partial}{\partial x} (x y^{2} - x^{3} y)

y^{2} - 3 y x^{2}

Solution steps

\frac{\partial}{\partial x} (x y^{2} - x^{3} 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^{3} y)

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

\frac{\partial}{\partial x} (x^{3} y) = 3 y x^{2}

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

4 cos (4 t)

f (x) = (2 x^{3} + 3)^{6}

\frac{d}{d x} (\frac{cos ( x )}{2})

- 2 x^{2}

What is (\partial)/(\partial x)(xy^2-x^3y) ?
The answer to (\partial)/(\partial x)(xy^2-x^3y) is y^2-3yx^2