What is (\partial)/(\partial y)(cos(x)+sin(y)) ?

The answer to (\partial)/(\partial y)(cos(x)+sin(y)) is cos(y)

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(\partial)/(\partial y)(cos(x)+sin(y))

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

cos (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + cos (y)

Simplify

= cos (y)

f (x) = 3 6 x + 8

\frac{d}{d x} (tan^{2} (sin (x)))

f (x) = x + 7

x = \frac{( y - 2 ) ^{2}}{3}, y = 8 - x

\frac{d}{d x} ((x^{2} + 2)^{- 5} cos (x))

What is (\partial)/(\partial y)(cos(x)+sin(y)) ?
The answer to (\partial)/(\partial y)(cos(x)+sin(y)) is cos(y)