What is (\partial)/(\partial y)(ye^x+sin(y)) ?

The answer to (\partial)/(\partial y)(ye^x+sin(y)) is e^x+cos(y)

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(\partial)/(\partial y)(ye^x+sin(y))

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

e^{x} + cos (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (sin (y)) = cos (y)

= e^{x} + cos (y)

What is (\partial)/(\partial y)(ye^x+sin(y)) ?
The answer to (\partial)/(\partial y)(ye^x+sin(y)) is e^x+cos(y)