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

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

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

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

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

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

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

= y - 4 y x

y^{^{'}} + y = e^{- 4 t} cos (3 t), y (0) = 0

x^{2} y^{^{'}} + x y = 3

e^{- 2 t + 3}

\int \frac{4}{θ ^{2}} cos (\frac{4}{θ}) d θ

\int \frac{1}{x ( x - 4 )} d x

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