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

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

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

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

2 x - 4

Solution steps

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

Simplify

(x - 2)^{2} + (y - 2)^{2} : x^{2} - 4 x + y^{2} + 8 - 4 y

= \frac{\partial}{\partial x} (x^{2} - 4 x + y^{2} + 8 - 4 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (8) - \frac{\partial}{\partial x} (4 y)

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

\frac{\partial}{\partial x} (4 x) = 4

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

\frac{\partial}{\partial x} (8) = 0

\frac{\partial}{\partial x} (4 y) = 0

= 2 x - 4 + 0 + 0 - 0

Simplify

= 2 x - 4

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