What is (\partial)/(\partial x)((z)(2xyz-e^z)) ?

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

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(\partial)/(\partial x)((z)(2xyz-e^z))

\frac{\partial}{\partial x} ((z) (2 x yz - e^{z}))

2 z^{2} y

Solution steps

\frac{\partial}{\partial x} ((z) (2 x yz - e^{z}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (2 x yz - e^{z})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (2 x yz) - \frac{\partial}{\partial x} (e^{z}))

\frac{\partial}{\partial x} (2 x yz) = 2 zy

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

= z (2 zy - 0)

Simplify

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

= 2 z^{2} y

\frac{4 x + 24}{( x - 2 ) ( x + 3 )}

\frac{x}{( x + 1 ) ( x + 4 )}

(2 sin (x) - 1)^{2}

- \frac{s ( - 2 s ^{2} - 5 )}{( s + 1 ) ( s - 1 ) ( s ^{2} + 1 )}

(x + \frac{1}{5}) (x - \frac{1}{5})

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