What is (\partial)/(\partial y)(e^{xy}-(x+1)cos(y)) ?

The answer to (\partial)/(\partial y)(e^{xy}-(x+1)cos(y)) is e^{xy}x+sin(y)(x+1)

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(\partial)/(\partial y)(e^{xy}-(x+1)cos(y))

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

e^{x y} x + sin (y) (x + 1)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= e^{x y} x + sin (y) (x + 1)

What is (\partial)/(\partial y)(e^{xy}-(x+1)cos(y)) ?
The answer to (\partial)/(\partial y)(e^{xy}-(x+1)cos(y)) is e^{xy}x+sin(y)(x+1)