What is (\partial)/(\partial x)((z)(4xyz-e^z)) ?

The answer to (\partial)/(\partial x)((z)(4xyz-e^z)) is 4z^2y

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(\partial)/(\partial x)((z)(4xyz-e^z))

\frac{\partial}{\partial x} ((z) (4 x yz - e^{z}))

4 z^{2} y

Solution steps

\frac{\partial}{\partial x} ((z) (4 x yz - e^{z}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (4 x yz - e^{z})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (4 x yz) - \frac{\partial}{\partial x} (e^{z}))

\frac{\partial}{\partial x} (4 x yz) = 4 zy

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

= z (4 zy - 0)

Simplify

z (4 zy - 0) : 4 z^{2} y

= 4 z^{2} y

\frac{4 s}{( s - 1 ) ( s + 1 ) ^{2}}

\frac{7 + 2 s + 6 e ^{- 4 s}}{( s + 2 ) ( s + 6 )}

(x + \frac{1}{6}) (x - \frac{1}{3})

\frac{e ^{x} x - 2 e ^{x}}{( x - 1 ) ^{2}}

\frac{( 3 + 4 i ) ^{4}}{( 2 - i ) ^{10}}

What is (\partial)/(\partial x)((z)(4xyz-e^z)) ?
The answer to (\partial)/(\partial x)((z)(4xyz-e^z)) is 4z^2y