What is (\partial)/(\partial x)(z^3-3xyz) ?

The answer to (\partial)/(\partial x)(z^3-3xyz) is -3zy

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(\partial)/(\partial x)(z^3-3xyz)

\frac{\partial}{\partial x} (z^{3} - 3 x yz)

- 3 zy

Solution steps

\frac{\partial}{\partial x} (z^{3} - 3 x yz)

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3 x yz) = 3 zy

= 0 - 3 zy

Simplify

= - 3 zy

\frac{\partial}{\partial x} (e^{9 x e^{y}})

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

\int csc^{9} (x) d x

x \to 0 lim (x^{2} - 3 x + 3)

\frac{d}{d x} (\frac{2 x}{x})

What is (\partial)/(\partial x)(z^3-3xyz) ?
The answer to (\partial)/(\partial x)(z^3-3xyz) is -3zy