What is (\partial)/(\partial y)(-xysin(x)+2ycos(x)) ?

The answer to (\partial)/(\partial y)(-xysin(x)+2ycos(x)) is -xsin(x)+2cos(x)

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(\partial)/(\partial y)(-xysin(x)+2ycos(x))

\frac{\partial}{\partial y} (- x y sin (x) + 2 y cos (x))

- x sin (x) + 2 cos (x)

Solution steps

\frac{\partial}{\partial y} (- x y sin (x) + 2 y cos (x))

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial y} (x y sin (x)) + \frac{\partial}{\partial y} (2 y cos (x))

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

\frac{\partial}{\partial y} (2 y cos (x)) = 2 cos (x)

= - x sin (x) + 2 cos (x)

\frac{d y}{d x} = \frac{( 1 + y )}{x}

(0.2) (1.5)

x \to 0 lim (\frac{2}{3 x ^{\frac{1}{3}}})

x

\int x ln (x^{2} + 1) + (x^{2} + 1) y d x

What is (\partial)/(\partial y)(-xysin(x)+2ycos(x)) ?
The answer to (\partial)/(\partial y)(-xysin(x)+2ycos(x)) is -xsin(x)+2cos(x)