What is (\partial)/(\partial x)(2x^4y+1) ?

The answer to (\partial)/(\partial x)(2x^4y+1) is 8x^3y

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(\partial)/(\partial x)(2x^4y+1)

\frac{\partial}{\partial x} (2 x^{4} y + 1)

8 x^{3} y

Solution steps

\frac{\partial}{\partial x} (2 x^{4} y + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{4} y) + \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (1) = 0

= 8 y x^{3} + 0

Simplify

= 8 x^{3} y

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What is (\partial)/(\partial x)(2x^4y+1) ?
The answer to (\partial)/(\partial x)(2x^4y+1) is 8x^3y