What is (\partial)/(\partial y)(-e^xsin(y)+1/y) ?

The answer to (\partial)/(\partial y)(-e^xsin(y)+1/y) is -e^xcos(y)-1/(y^2)

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(\partial)/(\partial y)(-e^xsin(y)+1/y)

\frac{\partial}{\partial y} (- e^{x} sin (y) + \frac{1}{y})

- e^{x} cos (y) - \frac{1}{y ^{2}}

Solution steps

\frac{\partial}{\partial y} (- e^{x} sin (y) + \frac{1}{y})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial y} (e^{x} sin (y)) + \frac{\partial}{\partial y} (\frac{1}{y})

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

\frac{\partial}{\partial y} (\frac{1}{y}) = - \frac{1}{y ^{2}}

= - e^{x} cos (y) - \frac{1}{y ^{2}}

What is (\partial)/(\partial y)(-e^xsin(y)+1/y) ?
The answer to (\partial)/(\partial y)(-e^xsin(y)+1/y) is -e^xcos(y)-1/(y^2)