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

The answer to (\partial)/(\partial x)((z)(x^2yz-e^z)) is 2z^2xy

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

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

2 z^{2} x y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (2 zy x - 0)

Simplify

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

= 2 z^{2} x y

, \frac{585}{13} + (28 - 15) \cdot 5

(a - 2) l e f t (a - 12)

\frac{n ( n + 1 ) ( n + 2 )}{3}

\frac{n ( n + 1 ) ( n + 2 )}{6}

(0.5 x + 0.4 y = 0.125) (1000)

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