What is (\partial)/(\partial z)(xye^z+x-z^2-3) ?

The answer to (\partial)/(\partial z)(xye^z+x-z^2-3) is e^zxy-2z

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(\partial)/(\partial z)(xye^z+x-z^2-3)

\frac{\partial}{\partial z} (x y e^{z} + x - z^{2} - 3)

e^{z} x y - 2 z

Solution steps

\frac{\partial}{\partial z} (x y e^{z} + x - z^{2} - 3)

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (x y e^{z}) + \frac{\partial}{\partial z} (x) - \frac{\partial}{\partial z} (z^{2}) - \frac{\partial}{\partial z} (3)

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

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

\frac{\partial}{\partial z} (z^{2}) = 2 z

\frac{\partial}{\partial z} (3) = 0

= x y e^{z} + 0 - 2 z - 0

Simplify

= e^{z} x y - 2 z

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What is (\partial)/(\partial z)(xye^z+x-z^2-3) ?
The answer to (\partial)/(\partial z)(xye^z+x-z^2-3) is e^zxy-2z