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

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

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

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

4 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (\frac{1}{2}) = 0

= 4 x + 0 + 0

Simplify

= 4 x

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