What is (\partial)/(\partial y)(sin(y)-ysin(x)) ?

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

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(\partial)/(\partial y)(sin(y)-ysin(x))

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

cos (y) - sin (x)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= cos (y) - sin (x)

\frac{d}{d x} (e^{x x^{2} + 1})

t \to 1 - lim (\frac{2 t}{t ^{2} - 1})

y^{^{''}} - 2 y + 4 y = 0

\int 11 x^{10} - \frac{10}{x ^{10}} d x

\int \frac{1}{9 - 4 x ^{2}} d x

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