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

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

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

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

z^{2} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (zy - 0)

Simplify

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

= z^{2} y

A (2, 0) y B (0, - 6)

(x - π)^{4}

\frac{7 x ^{3} + 16 x ^{2} + 20 x + 5}{( x ^{2} + 2 x + 2 ) ^{2}}

(x - \frac{1}{2}) (x + \frac{3}{4})

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