What is (\partial)/(\partial x)(x^2+xy+3y) ?

The answer to (\partial)/(\partial x)(x^2+xy+3y) is 2x+y

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(\partial)/(\partial x)(x^2+xy+3y)

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

2 x + y

Solution steps

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

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

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

\frac{\partial}{\partial x} (3 y) = 0

= 2 x + y + 0

Simplify

= 2 x + y

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What is (\partial)/(\partial x)(x^2+xy+3y) ?
The answer to (\partial)/(\partial x)(x^2+xy+3y) is 2x+y