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

The answer to (\partial)/(\partial x)((x^3-y^2)^2) is 6x^2(x^3-y^2)

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

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

6 x^{2} (x^{3} - y^{2})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 6 x^{2} (x^{3} - y^{2})

What is (\partial)/(\partial x)((x^3-y^2)^2) ?
The answer to (\partial)/(\partial x)((x^3-y^2)^2) is 6x^2(x^3-y^2)