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

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

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

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

3 z^{2} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (3 zy - 0)

Simplify

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

= 3 z^{2} y

\frac{3}{( x + 1 ) ^{2}}

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a (6, 5) a B (- 2, - 3)

\frac{( - 10 + x ^{2} + y ^{2} ) ^{2}}{4}

\frac{3 + 9 x}{( 1 + x ) ( 3 + 5 x )}

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