What is (\partial)/(\partial x)(2y^6+4y^8x^3) ?

The answer to (\partial)/(\partial x)(2y^6+4y^8x^3) is 12y^8x^2

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(\partial)/(\partial x)(2y^6+4y^8x^3)

\frac{\partial}{\partial x} (2 y^{6} + 4 y^{8} x^{3})

12 y^{8} x^{2}

Solution steps

\frac{\partial}{\partial x} (2 y^{6} + 4 y^{8} x^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 y^{6}) + \frac{\partial}{\partial x} (4 y^{8} x^{3})

\frac{\partial}{\partial x} (2 y^{6}) = 0

\frac{\partial}{\partial x} (4 y^{8} x^{3}) = 12 y^{8} x^{2}

= 0 + 12 y^{8} x^{2}

Simplify

= 12 y^{8} x^{2}

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What is (\partial)/(\partial x)(2y^6+4y^8x^3) ?
The answer to (\partial)/(\partial x)(2y^6+4y^8x^3) is 12y^8x^2