What is (\partial)/(\partial y)(1000-4xy+xy^2) ?

The answer to (\partial)/(\partial y)(1000-4xy+xy^2) is 2xy-4x

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(\partial)/(\partial y)(1000-4xy+xy^2)

\frac{\partial}{\partial y} (1000 - 4 x y + x y^{2})

2 x y - 4 x

Solution steps

\frac{\partial}{\partial y} (1000 - 4 x y + x y^{2})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (1000) - \frac{\partial}{\partial y} (4 x y) + \frac{\partial}{\partial y} (x y^{2})

\frac{\partial}{\partial y} (1000) = 0

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

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

= 0 - 4 x + 2 x y

Simplify

= 2 x y - 4 x

\frac{\partial}{\partial x} (e^{- 3 t} cos (π x))

\int_{0}^{\frac{5}{7}} 5 x - 7 x^{2} d x

x \to 0 + lim (x^{8 x})

\frac{3}{x - 4}

\frac{d}{d t} (9 t sin (π t))

What is (\partial)/(\partial y)(1000-4xy+xy^2) ?
The answer to (\partial)/(\partial y)(1000-4xy+xy^2) is 2xy-4x