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

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

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

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

y + 2

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

= y + 0 + 2 + 0

Simplify

= y + 2

f (θ) = θ cos (θ) sin (θ)

\frac{\partial}{\partial y} (y^{2} - 4 y + x y)

\int (4 x^{2} - 9 x)^{5} (8 x - 9) d x

x \to 0 lim (\frac{sin ^{3} ( x )}{x ^{2}})

n = 1 \sum \infty \frac{n}{e ^{4 n}}

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