What is the d/(dy)(ycos(x-y)) ?

The d/(dy)(ycos(x-y)) is cos(x-y)+ysin(x-y)

What is the first d/(dy)(ycos(x-y)) ?

The first d/(dy)(ycos(x-y)) is cos(x-y)+ysin(x-y)

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

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

Solution steps

\frac{d}{d 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{d y}{d y} cos (x - y) + \frac{d}{d y} (cos (x - y)) y

\frac{d y}{d y} = 1

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

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

Simplify

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

y = x^{3} + 6

\frac{s}{( s + 1 ) ( s + 2 )}

\frac{2}{s ^{2} + 6 s + 13}

3 sin (2 t + 5)

\frac{d}{d θ} (sec (θ))

What is the d/(dy)(ycos(x-y)) ?
The d/(dy)(ycos(x-y)) is cos(x-y)+ysin(x-y)
What is the first d/(dy)(ycos(x-y)) ?
The first d/(dy)(ycos(x-y)) is cos(x-y)+ysin(x-y)