What is (\partial)/(\partial z)(xe^{2y+3z}) ?

The answer to (\partial)/(\partial z)(xe^{2y+3z}) is xe^{2y+3z}*3

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(\partial)/(\partial z)(xe^{2y+3z})

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

x e^{2 y + 3 z} \cdot 3

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial z} (2 y + 3 z) = 3

= x e^{2 y + 3 z} \cdot 3

What is (\partial)/(\partial z)(xe^{2y+3z}) ?
The answer to (\partial)/(\partial z)(xe^{2y+3z}) is xe^{2y+3z}*3