What is (\partial)/(\partial x)(6x^4y-3xy+2y) ?

The answer to (\partial)/(\partial x)(6x^4y-3xy+2y) is 24x^3y-3y

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(\partial)/(\partial x)(6x^4y-3xy+2y)

\frac{\partial}{\partial x} (6 x^{4} y - 3 x y + 2 y)

24 x^{3} y - 3 y

Solution steps

\frac{\partial}{\partial x} (6 x^{4} y - 3 x y + 2 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x^{4} y) - \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (2 y)

\frac{\partial}{\partial x} (6 x^{4} y) = 24 y x^{3}

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

\frac{\partial}{\partial x} (2 y) = 0

= 24 y x^{3} - 3 y + 0

Simplify

= 24 x^{3} y - 3 y

What is (\partial)/(\partial x)(6x^4y-3xy+2y) ?
The answer to (\partial)/(\partial x)(6x^4y-3xy+2y) is 24x^3y-3y