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

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

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

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

2 x + y

Solution steps

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

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

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

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

= 2 x + y + 0

Simplify

= 2 x + y

\int \frac{2 x ^{2} + 6}{( x ^{2} - 2 x + 2 ) ^{2}} d x

x \to \infty lim (ln (2 x))

x = - 1, x = 3, y = x^{3} - 1, y = 0

\frac{d}{d x} (x^{8} ln (5 x))

\frac{d}{d x} (1200 x^{2} - 0.2 x)

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