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

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

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

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

2 x + y

Solution steps

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

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

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

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

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

= 2 x + 0 + y

Simplify

= 2 x + y

\frac{d}{d x} (5 - 5 sin (x))

f (x) = 2 cos (2 x)

(2 x + 3 y) d x + (6 x + 9 y - 3) d y = 0

\int d (x y)

\frac{\partial}{\partial y} (y^{3} + 2 y e^{x})

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