DERIVATIVE OF COT SQUARE ROOT OF X

We know the derivative of cotx, which is -csc²x.

(cotx)' = -csc²x

We can find the derivative of cot(√x) using chain rule.

If y = cot(√x), find ᵈʸ⁄dₓ.

Let u = √x.

Then, we have

y = cotu

Now, y = cotu and u = √x. That is, y is a function of u and u is a function of x.  

By chain rule, the derivative of y with respect to x,

Substitute y = cotu and u = √x.

Substitute u = √x.

Therefore,

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