What is (\partial)/(\partial y)(1000+11x+6y+xy-(x-3)^2-(y-4)^2) ?

The answer to (\partial)/(\partial y)(1000+11x+6y+xy-(x-3)^2-(y-4)^2) is x+14-2y

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(\partial)/(\partial y)(1000+11x+6y+xy-(x-3)^2-(y-4)^2)

\frac{\partial}{\partial y} (1000 + 11 x + 6 y + x y - (x - 3)^{2} - (y - 4)^{2})

x + 14 - 2 y

Solution steps

\frac{\partial}{\partial y} (1000 + 11 x + 6 y + x y - (x - 3)^{2} - (y - 4)^{2})

Simplify

1000 + 11 x + 6 y + x y - (x - 3)^{2} - (y - 4)^{2} : - x^{2} + x y + 17 x + 14 y + 975 - y^{2}

= \frac{\partial}{\partial y} (- x^{2} + x y + 17 x + 14 y + 975 - y^{2})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial y} (x^{2}) + \frac{\partial}{\partial y} (x y) + \frac{\partial}{\partial y} (17 x) + \frac{\partial}{\partial y} (14 y) + \frac{\partial}{\partial y} (975) - \frac{\partial}{\partial y} (y^{2})

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

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

\frac{\partial}{\partial y} (17 x) = 0

\frac{\partial}{\partial y} (14 y) = 14

\frac{\partial}{\partial y} (975) = 0

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

= - 0 + x + 0 + 14 + 0 - 2 y

Simplify

= x + 14 - 2 y

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What is (\partial)/(\partial y)(1000+11x+6y+xy-(x-3)^2-(y-4)^2) ?
The answer to (\partial)/(\partial y)(1000+11x+6y+xy-(x-3)^2-(y-4)^2) is x+14-2y