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

The answer to (\partial)/(\partial x)((x-2)^2+(5-x-y)^2) is 4x+2y-14

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

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

4 x + 2 y - 14

Solution steps

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

Simplify

(x - 2)^{2} + (5 - x - y)^{2} : 2 x^{2} + 2 x y - 14 x + y^{2} + 29 - 10 y

= \frac{\partial}{\partial x} (2 x^{2} + 2 x y - 14 x + y^{2} + 29 - 10 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{2}) + \frac{\partial}{\partial x} (2 x y) - \frac{\partial}{\partial x} (14 x) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (29) - \frac{\partial}{\partial x} (10 y)

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

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

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

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

\frac{\partial}{\partial x} (29) = 0

\frac{\partial}{\partial x} (10 y) = 0

= 4 x + 2 y - 14 + 0 + 0 - 0

Simplify

= 4 x + 2 y - 14

x \to 7 lim (- x^{2} + 3 x - 8)

\frac{\partial}{\partial x} (8 x^{6} y^{4} + 9 x^{5} y^{7})

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

f (x) = sech (x)

(\frac{x ^{2} + 5}{x ^{2} - 5})^{2}

What is (\partial)/(\partial x)((x-2)^2+(5-x-y)^2) ?
The answer to (\partial)/(\partial x)((x-2)^2+(5-x-y)^2) is 4x+2y-14