What is (\partial)/(\partial x)(4x^2y+4xy^2) ?

The answer to (\partial)/(\partial x)(4x^2y+4xy^2) is 8yx+4y^2

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(\partial)/(\partial x)(4x^2y+4xy^2)

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

8 y x + 4 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

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

= 8 y x + 4 y^{2}

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What is (\partial)/(\partial x)(4x^2y+4xy^2) ?
The answer to (\partial)/(\partial x)(4x^2y+4xy^2) is 8yx+4y^2