What is (\partial)/(\partial x)(7x^2y+5xy^3) ?

The answer to (\partial)/(\partial x)(7x^2y+5xy^3) is 14yx+5y^3

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(\partial)/(\partial x)(7x^2y+5xy^3)

\frac{\partial}{\partial x} (7 x^{2} y + 5 x y^{3})

14 y x + 5 y^{3}

Solution steps

\frac{\partial}{\partial x} (7 x^{2} y + 5 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (7 x^{2} y) + \frac{\partial}{\partial x} (5 x y^{3})

\frac{\partial}{\partial x} (7 x^{2} y) = 14 y x

\frac{\partial}{\partial x} (5 x y^{3}) = 5 y^{3}

= 14 y x + 5 y^{3}

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What is (\partial)/(\partial x)(7x^2y+5xy^3) ?
The answer to (\partial)/(\partial x)(7x^2y+5xy^3) is 14yx+5y^3