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

The answer to (\partial)/(\partial x)((x+xy+y)^3) is 3(x+xy+y)^2(y+1)

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

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

3 (x + x y + y)^{2} (y + 1)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= 3 (x + x y + y)^{2} (y + 1)

What is (\partial)/(\partial x)((x+xy+y)^3) ?
The answer to (\partial)/(\partial x)((x+xy+y)^3) is 3(x+xy+y)^2(y+1)