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

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

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

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

6 x^{2} + 6 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

\frac{\partial}{\partial x} (6 x y) = 6 y

\frac{\partial}{\partial x} (2 y^{4}) = 0

= 6 x^{2} + 6 y - 0

Simplify

= 6 x^{2} + 6 y

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