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

The answer to (\partial)/(\partial x)(4x-sqrt(2y^2+z^2)) is 4

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(\partial)/(\partial x)(4x-sqrt(2y^2+z^2))

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

4

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 4 - 0

Simplify

= 4

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