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

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

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

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

2 y + x + 3

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

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

= 2 y + x + 3 + 0 + 0

Simplify

= 2 y + x + 3

f (x) = 6 tan (x)

x \to 2 lim (\frac{1}{( x - 2 ) ^{2}})

w (z) = 6 z^{2} e^{z}

\int_{0}^{l n (2)} \int_{1}^{l n (5)} e^{2 x + y} d y d x

\frac{d}{d x} (\frac{1 - x}{( x + 1 ) ^{3}})

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