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

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

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

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

8 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 8 x + 0

Simplify

= 8 x

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