What is (\partial)/(\partial x)(3x^2y+6xy^3) ?

The answer to (\partial)/(\partial x)(3x^2y+6xy^3) is 6yx+6y^3

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(\partial)/(\partial x)(3x^2y+6xy^3)

\frac{\partial}{\partial x} (3 x^{2} y + 6 x y^{3})

6 y x + 6 y^{3}

Solution steps

\frac{\partial}{\partial x} (3 x^{2} y + 6 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x^{2} y) + \frac{\partial}{\partial x} (6 x y^{3})

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

\frac{\partial}{\partial x} (6 x y^{3}) = 6 y^{3}

= 6 y x + 6 y^{3}

What is (\partial)/(\partial x)(3x^2y+6xy^3) ?
The answer to (\partial)/(\partial x)(3x^2y+6xy^3) is 6yx+6y^3