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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

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