What is (\partial)/(\partial x)(2x^4y^3+y) ?

The answer to (\partial)/(\partial x)(2x^4y^3+y) is 8x^3y^3

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(\partial)/(\partial x)(2x^4y^3+y)

\frac{\partial}{\partial x} (2 x^{4} y^{3} + y)

8 x^{3} y^{3}

Solution steps

\frac{\partial}{\partial x} (2 x^{4} y^{3} + y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{4} y^{3}) + \frac{\partial}{\partial x} (y)

\frac{\partial}{\partial x} (2 x^{4} y^{3}) = 8 y^{3} x^{3}

\frac{\partial}{\partial x} (y) = 0

= 8 y^{3} x^{3} + 0

Simplify

= 8 x^{3} y^{3}

What is (\partial)/(\partial x)(2x^4y^3+y) ?
The answer to (\partial)/(\partial x)(2x^4y^3+y) is 8x^3y^3