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

The answer to (\partial)/(\partial x)((z)(x^2+y^2+z^2)) is 2zx

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

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

2 z x

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= z (2 x + 0 + 0)

Simplify

= 2 z x

(2 + 3 i)^{4}

(- 3 + i)^{5}

x (x + 1)

(2 + 3 - 2 - 3)^{6}

(x^{2} + y^{2}) x^{2} + y^{2}

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