What is (\partial)/(\partial x)(y+3xz+x^3) ?

The answer to (\partial)/(\partial x)(y+3xz+x^3) is 3x^2+3z

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(\partial)/(\partial x)(y+3xz+x^3)

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

3 x^{2} + 3 z

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 + 3 z + 3 x^{2}

Simplify

= 3 x^{2} + 3 z

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