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

The answer to (\partial)/(\partial x)((x+y)(xy+1)) is y^2+2xy+1

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(\partial)/(\partial x)((x+y)(xy+1))

\frac{\partial}{\partial x} ((x + y) (x y + 1))

y^{2} + 2 x y + 1

Solution steps

\frac{\partial}{\partial x} ((x + y) (x y + 1))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + y, g = x y + 1

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

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

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

= 1 \cdot (x y + 1) + y (x + y)

Simplify

1 \cdot (x y + 1) + y (x + y) : y^{2} + 2 x y + 1

= y^{2} + 2 x y + 1

\int x^{2} + 6 x + 11 d x

\int sin^{2} (x) sin (3 x) d x

\frac{\partial}{\partial x} (x + 4)

\frac{1}{2 s ^{3} + 6 s ^{2} + 4 s}

\int x (x) d x

What is (\partial)/(\partial x)((x+y)(xy+1)) ?
The answer to (\partial)/(\partial x)((x+y)(xy+1)) is y^2+2xy+1