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Question

Find derivative with respect to x of 2√cot(x2​​​) ? Please give in detail

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Solution

y equals 2 square root of c o t space x squared end root fraction numerator d y over denominator d x end fraction equals fraction numerator 2 over denominator 2 square root of c o t space x squared end root end fraction. fraction numerator d over denominator d x end fraction left parenthesis c o t space x squared right parenthesis left square bracket A p p l y i n g space c h a i n space r u l e right square bracket space equals fraction numerator 1 over denominator square root of c o t space x squared end root end fraction. negative cos e c squared x squared. fraction numerator d over denominator d x end fraction x squared equals fraction numerator negative 2 x space cos e c squared x squared over denominator square root of c o t space x squared end root end fraction
As per your doubt, we can see that both answers are the different. But basically, both the answers are the same. In Sinadin's answer,he changed the answer, by converting cosec and cot functions and rearranging them, to make it a function containing sine and cosine functions.

So both the answers are correct and you will get marks for writing any of them. I prefer the method that i chose, because it is simple and not complicated as the 2nd one

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