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

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

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

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

2 y + 3 x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y + 3 x^{2}

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