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

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

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

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

3 y^{2} x^{2} - 2 y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 3 y^{2} x^{2} - 2 y^{3}

x \to 2 lim (\frac{1}{x ^{2} - 4})

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

\int_{3}^{9} 1 + x^{4} + 2 x^{2} d x

\int (b - x)^{2} d x

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