What is (\partial)/(\partial x)((x^2y-y^3)^5) ?

The answer to (\partial)/(\partial x)((x^2y-y^3)^5) is 10xy(x^2y-y^3)^4

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(\partial)/(\partial x)((x^2y-y^3)^5)

\frac{\partial}{\partial x} ((x^{2} y - y^{3})^{5})

10 x y (x^{2} y - y^{3})^{4}

Solution steps

\frac{\partial}{\partial x} ((x^{2} y - y^{3})^{5})

Treat

y

as a constant

Apply the chain rule:

5 (x^{2} y - y^{3})^{4} \frac{\partial}{\partial x} (x^{2} y - y^{3})

= 5 (x^{2} y - y^{3})^{4} \frac{\partial}{\partial x} (x^{2} y - y^{3})

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

= 5 (x^{2} y - y^{3})^{4} \cdot 2 y x

Simplify

= 10 x y (x^{2} y - y^{3})^{4}

What is (\partial)/(\partial x)((x^2y-y^3)^5) ?
The answer to (\partial)/(\partial x)((x^2y-y^3)^5) is 10xy(x^2y-y^3)^4