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

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

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

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

3 y x^{2} + 2 y^{3}

Solution steps

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

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

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

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

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