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

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

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

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

2 x + y

Solution steps

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

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

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

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

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

= 2 x + y + 0 + 0

Simplify

= 2 x + y

\int_{0}^{\frac{π}{2}} (sin (x))^{2} d x

e^{- 2 t} \cdot sin (t)

\frac{\partial}{\partial y} (y sin (z))

x \to 0 lim ((tan (5 x))^{x})

\frac{1}{s ^{2} + 2 s + 2}

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