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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

\frac{d y}{d x} = \frac{cos ( 9 x )}{e ^{9 y}}

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

\int \frac{4 x ^{2} - 2}{x ^{3} - x} d x

\int x^{\frac{1}{3}} + 3 d x

\frac{\partial}{\partial x} (x sin (y) + z e^{x})

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