 Hi and how are you all today? The question says differentiate cot inverse 1 minus x upon 1 plus x with respect to x. So here let y be equal to cot inverse 1 minus x upon 1 plus x. So this can be written as cot y equal to 1 minus x upon 1 plus x right. Further we can also write it as tan y is equal to now it will be 1 plus x upon 1 minus x. That further implies y is equal to tan inverse 1 plus x upon 1 minus x. Now put x equal to tan theta. So therefore theta will be equal to tan inverse x right. So we can write it as y equal to tan inverse 1 plus tan theta upon 1 minus tan theta. That is equal to tan inverse. Now in place of 1 plus tan theta upon 1 minus tan theta we can write tan theta plus pi by 4. So we have y equal to these two will get cancelled and we are left with theta plus pi by 4. Theta is equal to what? It is equal to tan inverse x. So we have on differentiating it dy by dx is equal to dy by dx of tan inverse x plus dy sorry dy dx of pi by 4. Since pi by 4 is a constant we have dy by dx equal to derivative of tan inverse x is equal to 1 upon 1 plus x square plus derivative of a constant is equal to 0. So we have the answer to the given question as dy by dx is equal to 1 upon 1 plus x square right. So this is the answer to the given question. Hope you understood it well and enjoyed it too. Have a nice day ahead.