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

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

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

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

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

Solution steps

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

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

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

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

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

y^{^{'}} = (4 y + 21)^{(\frac{1}{2})}

\frac{d y}{d x} = - y

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

6 t^{2} y^{^{''}} - 12 y = 14 t^{2} - 1

\int \frac{x}{( x + 1 ) ( x + 2 ) ( x + 3 )} d x

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