What is (\partial)/(\partial y)(xy-5y+x^2+y^2-10x) ?

The answer to (\partial)/(\partial y)(xy-5y+x^2+y^2-10x) is x+2y-5

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(\partial)/(\partial y)(xy-5y+x^2+y^2-10x)

\frac{\partial}{\partial y} (x y - 5 y + x^{2} + y^{2} - 10 x)

x + 2 y - 5

Solution steps

\frac{\partial}{\partial y} (x y - 5 y + x^{2} + y^{2} - 10 x)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x y) - \frac{\partial}{\partial y} (5 y) + \frac{\partial}{\partial y} (x^{2}) + \frac{\partial}{\partial y} (y^{2}) - \frac{\partial}{\partial y} (10 x)

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

\frac{\partial}{\partial y} (5 y) = 5

\frac{\partial}{\partial y} (x^{2}) = 0

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

\frac{\partial}{\partial y} (10 x) = 0

= x - 5 + 0 + 2 y - 0

Simplify

= x + 2 y - 5

What is (\partial)/(\partial y)(xy-5y+x^2+y^2-10x) ?
The answer to (\partial)/(\partial y)(xy-5y+x^2+y^2-10x) is x+2y-5