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

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

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

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

3 x^{2}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y^{3}) = 0

\frac{\partial}{\partial x} (z^{3}) = 0

= 3 x^{2} + 0 + 0

Simplify

= 3 x^{2}

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