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

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

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

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

4 y x + 3 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 4 y x + 3 y^{2}

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