What is (\partial)/(\partial x)(x^2z+3z^2x+6(x+z)) ?

The answer to (\partial)/(\partial x)(x^2z+3z^2x+6(x+z)) is 2zx+3z^2+6

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(\partial)/(\partial x)(x^2z+3z^2x+6(x+z))

\frac{\partial}{\partial x} (x^{2} z + 3 z^{2} x + 6 (x + z))

2 z x + 3 z^{2} + 6

Solution steps

\frac{\partial}{\partial x} (x^{2} z + 3 z^{2} x + 6 (x + z))

Treat

z

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} z) + \frac{\partial}{\partial x} (3 z^{2} x) + \frac{\partial}{\partial x} (6 (x + z))

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

\frac{\partial}{\partial x} (3 z^{2} x) = 3 z^{2}

\frac{\partial}{\partial x} (6 (x + z)) = 6

= 2 z x + 3 z^{2} + 6

What is (\partial)/(\partial x)(x^2z+3z^2x+6(x+z)) ?
The answer to (\partial)/(\partial x)(x^2z+3z^2x+6(x+z)) is 2zx+3z^2+6