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

The answer to (\partial)/(\partial y)((x-3)^2+(y-4)^2) is 2y-8

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(\partial)/(\partial y)((x-3)^2+(y-4)^2)

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

2 y - 8

Solution steps

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

Simplify

(x - 3)^{2} + (y - 4)^{2} : x^{2} - 6 x + y^{2} + 25 - 8 y

= \frac{\partial}{\partial y} (x^{2} - 6 x + y^{2} + 25 - 8 y)

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} (6 x) + \frac{\partial}{\partial y} (y^{2}) + \frac{\partial}{\partial y} (25) - \frac{\partial}{\partial y} (8 y)

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

\frac{\partial}{\partial y} (6 x) = 0

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

\frac{\partial}{\partial y} (25) = 0

\frac{\partial}{\partial y} (8 y) = 8

= 0 - 0 + 2 y + 0 - 8

Simplify

= 2 y - 8

\int_{- 1}^{1} x^{100} d x

\frac{5}{1 - x ^{2}}

\frac{d}{d x} ((3 x^{4}) (2 x^{5}))

\int e^{3 x - 5} d x

\frac{d}{d x} (\frac{3 x + 1}{2 x - 5})

What is (\partial)/(\partial y)((x-3)^2+(y-4)^2) ?
The answer to (\partial)/(\partial y)((x-3)^2+(y-4)^2) is 2y-8