# What is the derivative of # y=sinx/(2+cosx)#?

This function can be differentiated using the "quotient rule":

We can rearrange it to get:

Let's apply this rearranged identity:

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To find the derivative of ( y = \frac{\sin(x)}{2 + \cos(x)} ), you can use the quotient rule, which states that if ( y = \frac{u}{v} ), then ( y' = \frac{u'v - uv'}{v^2} ), where ( u' ) and ( v' ) are the derivatives of ( u ) and ( v ) respectively.

Let ( u = \sin(x) ) and ( v = 2 + \cos(x) ).

Then, ( u' = \cos(x) ) and ( v' = -\sin(x) ).

Now apply the quotient rule:

[ y' = \frac{\sin(x)(-\sin(x)) - \cos(x)\cos(x)}{(2 + \cos(x))^2} ]

[ = \frac{-\sin^2(x) - \cos^2(x)}{(2 + \cos(x))^2} ]

[ = \frac{-1}{(2 + \cos(x))^2} ]

So, the derivative of ( y = \frac{\sin(x)}{2 + \cos(x)} ) is ( y' = \frac{-1}{(2 + \cos(x))^2} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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