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)

x \to \infty lim (\frac{1}{3 x})

x \to - 2 lim (\frac{x - 2}{x ^{2} - 4})

\frac{5 - x}{( 4 x ^{2} + 1 ) ^{3}}

\frac{d P}{d t} = 5 Pt, P (1) = 6

\frac{d}{d x} (\frac{( 7 - 5 x )}{cos ( 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)