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

The answer to (\partial)/(\partial x)(x+xy+y) is y+1

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

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

y + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

= 1 + y + 0

Simplify

= y + 1

y^{^{'}} = (1 - 2 x) y^{2}

\frac{d}{d x} (4 x e^{2 x})

\frac{d}{d x} (\frac{x - 1}{x + 4})

\int cos (5 x) cos (2 x) d x

\int_{1}^{3} (x^{2} - \frac{1}{4 x ^{2}}) d x

What is (\partial)/(\partial x)(x+xy+y) ?
The answer to (\partial)/(\partial x)(x+xy+y) is y+1