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

The answer to (\partial)/(\partial x)((z)(e^z-3xyz)) is -3z^2y

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

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

- 3 z^{2} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (0 - 3 zy)

Simplify

z (0 - 3 zy) : - 3 z^{2} y

= - 3 z^{2} y

\frac{2 x ^{2} - 8 x - 8}{( x - 2 ) ( x ^{2} + 4 )}

F (- 3, - 2)

(\frac{x ^{2}}{2} + \frac{2}{x})^{6}

π + 2 (1 + t) (2 + 2 t)

(2 - 8 x^{2} - 2 x) - (7 x^{3} + 3 x = 5 x^{2})

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