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

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

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

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

y^{3} + 2 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= y^{3} + 2 x

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