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

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

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

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

2 x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (5 y^{3}) = 0

= 2 y x + 0

Simplify

= 2 x y

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