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

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

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

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

- y cos (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - y cos (x)

Simplify

= - y cos (x)

f (x) = 3 x^{3} - x^{2} + 2, (1, 4)

\int t^{3} \cdot ln (t^{2}) d t

\frac{\partial}{\partial y} (x y^{3} - x^{2})

\frac{\partial}{\partial y} (x e^{- x^{2} y})

\int \frac{5 x ^{4}}{x ^{5} - 3} d x

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