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

The answer to (\partial)/(\partial x)((x-3)^2+(y-2)^2) is 2x-6

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

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

2 x - 6

Solution steps

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

Simplify

(x - 3)^{2} + (y - 2)^{2} : x^{2} - 6 x + y^{2} + 13 - 4 y

= \frac{\partial}{\partial x} (x^{2} - 6 x + y^{2} + 13 - 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} (6 x) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (13) - \frac{\partial}{\partial x} (4 y)

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

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

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

\frac{\partial}{\partial x} (13) = 0

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

= 2 x - 6 + 0 + 0 - 0

Simplify

= 2 x - 6

{\frac{1}{s ^{4} - 9}}

- 5 t + 3 + t^{7}

\int_{- 2}^{2} t^{3} (3 + t^{4})^{3} d t

h \to + 0 lim (\frac{h}{sin ( 3 h )})

What is (\partial)/(\partial x)((x-3)^2+(y-2)^2) ?
The answer to (\partial)/(\partial x)((x-3)^2+(y-2)^2) is 2x-6