What is (\partial)/(\partial x)((z)(8xyz-e^z)) ?

The answer to (\partial)/(\partial x)((z)(8xyz-e^z)) is 8z^2y

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(\partial)/(\partial x)((z)(8xyz-e^z))

\frac{\partial}{\partial x} ((z) (8 x yz - e^{z}))

8 z^{2} y

Solution steps

\frac{\partial}{\partial x} ((z) (8 x yz - e^{z}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (8 x yz - e^{z})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (8 x yz) - \frac{\partial}{\partial x} (e^{z}))

\frac{\partial}{\partial x} (8 x yz) = 8 zy

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

= z (8 zy - 0)

Simplify

z (8 zy - 0) : 8 z^{2} y

= 8 z^{2} y

lo g_{10} (x^{- 3} y^{2})

(2 x - 3 i)^{2}

(5 x + 4 + 14)^{2}

\frac{- 1}{3} 3^{2} + \frac{2}{3} 3 + \frac{8}{3}

(e^{- x} + 1)^{2}

What is (\partial)/(\partial x)((z)(8xyz-e^z)) ?
The answer to (\partial)/(\partial x)((z)(8xyz-e^z)) is 8z^2y