What is (\partial)/(\partial z)(2ysin(x)+e^{2z}) ?

The answer to (\partial)/(\partial z)(2ysin(x)+e^{2z}) is 2e^{2z}

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(\partial)/(\partial z)(2ysin(x)+e^{2z})

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

2 e^{2 z}

Solution steps

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

Treat

y, x

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial z} (2 y sin (x)) = 0

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

= 0 + e^{2 z} \cdot 2

Simplify

= 2 e^{2 z}

What is (\partial)/(\partial z)(2ysin(x)+e^{2z}) ?
The answer to (\partial)/(\partial z)(2ysin(x)+e^{2z}) is 2e^{2z}