What is (\partial)/(\partial x)(x^2+y^2+(12-x-y)^2) ?

The answer to (\partial)/(\partial x)(x^2+y^2+(12-x-y)^2) is 4x+2y-24

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(\partial)/(\partial x)(x^2+y^2+(12-x-y)^2)

\frac{\partial}{\partial x} (x^{2} + y^{2} + (12 - x - y)^{2})

4 x + 2 y - 24

Solution steps

\frac{\partial}{\partial x} (x^{2} + y^{2} + (12 - x - y)^{2})

Simplify

x^{2} + y^{2} + (12 - x - y)^{2} : 2 x^{2} + 2 x y - 24 x + 2 y^{2} - 24 y + 144

= \frac{\partial}{\partial x} (2 x^{2} + 2 x y - 24 x + 2 y^{2} - 24 y + 144)

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} (24 x) + \frac{\partial}{\partial x} (2 y^{2}) - \frac{\partial}{\partial x} (24 y) + \frac{\partial}{\partial x} (144)

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

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

\frac{\partial}{\partial x} (24 x) = 24

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

\frac{\partial}{\partial x} (24 y) = 0

\frac{\partial}{\partial x} (144) = 0

= 4 x + 2 y - 24 + 0 - 0 + 0

Simplify

= 4 x + 2 y - 24

\frac{\partial}{\partial x} (x y e^{- y})

x \to l n (2) lim (- 4 e^{- 2 x})

\int 9 x e^{x} d x

y^{^{''}} + 4 \cdot y = cos (x)

\frac{d}{d x} (\frac{x}{x ^{2} + 225})

What is (\partial)/(\partial x)(x^2+y^2+(12-x-y)^2) ?
The answer to (\partial)/(\partial x)(x^2+y^2+(12-x-y)^2) is 4x+2y-24