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

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

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

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

4 x + 2 y

Solution steps

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

Simplify

x^{2} + y^{2} + (x + y)^{2} : 2 x^{2} + 2 x y + 2 y^{2}

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

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} (2 y^{2})

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

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

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

= 4 x + 2 y + 0

Simplify

= 4 x + 2 y

\frac{\partial}{\partial x} (\frac{1}{( 1 + e ^{- x} )})

\frac{d}{d x} (lo g_{10} ((x - 3)^{2}))

\int \frac{4 x ^{2} + 1}{2 x + 5} d x

\int e^{- \frac{3}{2} t} d t

3 x^{2} + 4 x + 8

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