What is (\partial)/(\partial x)(x^4y^2-x^3y) ?

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

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(\partial)/(\partial x)(x^4y^2-x^3y)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 4 y^{2} x^{3} - 3 y x^{2}

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