What is (\partial)/(\partial x)(xcos(xy)-2y) ?

The answer to (\partial)/(\partial x)(xcos(xy)-2y) is cos(xy)-xysin(xy)

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(\partial)/(\partial x)(xcos(xy)-2y)

\frac{\partial}{\partial x} (x cos (x y) - 2 y)

cos (x y) - x y sin (x y)

Solution steps

\frac{\partial}{\partial x} (x cos (x y) - 2 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x cos (x y)) - \frac{\partial}{\partial x} (2 y)

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

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

= cos (y x) - y x sin (y x) - 0

Simplify

= cos (x y) - x y sin (x y)

What is (\partial)/(\partial x)(xcos(xy)-2y) ?
The answer to (\partial)/(\partial x)(xcos(xy)-2y) is cos(xy)-xysin(xy)