# How do you find the derivative of #y=cos(x)/csc(x)#?

At this point, we could stop, but by using the trigonometric double-angle identities, we find further that...

Thus, for full simplification, we arrive at...

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To find the derivative of ( y = \frac{\cos(x)}{\csc(x)} ), you can use the quotient rule, which states that if you have a function in the form ( \frac{u(x)}{v(x)} ), then its derivative is given by ( \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2} ). Applying this rule to the given function, the derivative is:

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

After simplifying, you can express the derivative as:

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

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