 Hi and welcome to the session, I am Deepika here. Let's discuss the question, differentiate the following function with respect to x, 2 into under root of cot of x square. So let's start the solution. Let y is equal to our given function, y is equal to 2 into under root of cot of x square. This can be written as y is equal to 2 into cot x square raised to power 1 by 2. Differentiate both sides with respect to x. We have dy by dx is equal to 2 into 1 by 2 into cot of x square raised to power minus 1 by 2 into dy by dx of cot x square. In this step, we have applied the chain rule. Now we know that derivative of cot theta is minus cosecant square theta. So this is equal to cot x square raised to power minus 1 by 2 into minus cosecant square x square into dy by dx of x square that is 2x. Therefore, this is equal to minus 2x into cosecant square x square upon under root of cot of x square. Again this is equal to minus 2x upon sine square x square upon. Now cot theta is equal to cos theta upon sine theta. So under root of cot of x square is equal to under root of cos of x square upon under root of sine of x square. This is equal to minus 2x upon sine square x square into under root of sine x square upon under root of cos x square. And this is equal to minus 2x into under root of sine x square upon sine x square into sine x square into under root of cos x square. So this is equal to minus 2x upon sine x square into under root of sine x square into under root of cos x square. Now multiply the numerator and denominator by root 2 because we want the formula of sine 2 theta here. As we know sine 2 theta is equal to 2 sine theta cos theta. So this is equal to minus 2 root 2x upon sine x square into root 2 into under root of sine x square into under root of cos x square. So this is equal to minus 2 root 2x upon sine x square into under root of 2 sine x square into cos x square. Now this is equal to minus 2 root 2x upon sine x square into under root of sine 2x square because sine 2 theta is equal to 2 sine theta into cos theta. Hence the derivative of the above function is minus 2 root 2x upon sine x square into under root of sine 2x square and this is our answer for the above question. I hope the solution is clear to you. Bye and take care.