What is (\partial)/(\partial y)(x^4y-2x^3y^2) ?

The answer to (\partial)/(\partial y)(x^4y-2x^3y^2) is x^4-4x^3y

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(\partial)/(\partial y)(x^4y-2x^3y^2)

\frac{\partial}{\partial y} (x^{4} y - 2 x^{3} y^{2})

x^{4} - 4 x^{3} y

Solution steps

\frac{\partial}{\partial y} (x^{4} y - 2 x^{3} y^{2})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{4} y) - \frac{\partial}{\partial y} (2 x^{3} y^{2})

\frac{\partial}{\partial y} (x^{4} y) = x^{4}

\frac{\partial}{\partial y} (2 x^{3} y^{2}) = 4 x^{3} y

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

x^{5} + 1

10 y^{^{''}} + 1000 y = 170 cos (8 t)

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

\int x^{3} - 4 x^{2} + C d x

2 x^{2} + 2

What is (\partial)/(\partial y)(x^4y-2x^3y^2) ?
The answer to (\partial)/(\partial y)(x^4y-2x^3y^2) is x^4-4x^3y