What is (\partial)/(\partial y)(ycos(x-y)) ?

The answer to (\partial)/(\partial y)(ycos(x-y)) is cos(x-y)+ysin(x-y)

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(\partial)/(\partial y)(ycos(x-y))

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = cos (x - y)

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

\frac{\partial}{\partial y} (y) = 1

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

= 1 \cdot cos (x - y) + sin (x - y) y

Simplify

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

What is (\partial)/(\partial y)(ycos(x-y)) ?
The answer to (\partial)/(\partial y)(ycos(x-y)) is cos(x-y)+ysin(x-y)