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

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

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

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

2 x + 2 y

Solution steps

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

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

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

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

= 2 x - 0 + 2 y

Simplify

= 2 x + 2 y

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