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

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

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

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

2 x + 2 y

Solution steps

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

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

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

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

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

= 2 x + 2 y + 0

Simplify

= 2 x + 2 y

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = e^{2 x}

\frac{d}{d x} (lo g_{x} (3))

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

\frac{1}{( s ^{2} + 4 ) ^{2}}

\frac{d}{d t} (5 t^{- 3})

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