What is (\partial)/(\partial y)(0.5x^2+y^2-3x+2y-5) ?

The answer to (\partial)/(\partial y)(0.5x^2+y^2-3x+2y-5) is 2y+2

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(\partial)/(\partial y)(0.5x^2+y^2-3x+2y-5)

\frac{\partial}{\partial y} (0.5 x^{2} + y^{2} - 3 x + 2 y - 5)

2 y + 2

Solution steps

\frac{\partial}{\partial y} (0.5 x^{2} + y^{2} - 3 x + 2 y - 5)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (0.5 x^{2}) + \frac{\partial}{\partial y} (y^{2}) - \frac{\partial}{\partial y} (3 x) + \frac{\partial}{\partial y} (2 y) - \frac{\partial}{\partial y} (5)

\frac{\partial}{\partial y} (0.5 x^{2}) = 0

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

\frac{\partial}{\partial y} (3 x) = 0

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

\frac{\partial}{\partial y} (5) = 0

= 0 + 2 y - 0 + 2 - 0

Simplify

= 2 y + 2

What is (\partial)/(\partial y)(0.5x^2+y^2-3x+2y-5) ?
The answer to (\partial)/(\partial y)(0.5x^2+y^2-3x+2y-5) is 2y+2