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

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

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

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

2 y - 2 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 y - 2 x + 0

Simplify

= 2 y - 2 x

\int_{0}^{1} π (4 - \frac{3}{2} x)^{2} d x

x \to \infty lim (\frac{10 x + 100}{x ^{2} - 30})

y (t + 2) y^{^{'}} + 1 = - t

\int_{0}^{2} 2 π (3 - x) (8 - x^{3}) d x

\frac{d}{d x} ((x)^{2} (4 x + 1))

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