 Hi, and welcome to the session, I am Deepika here. Let's discuss the question, differentiate the following with respect to x, sign of tan inverse e raise to power minus x. So let's start the solution. Here we will use a chain rule, let y is equal to sin u, where u is equal to tan inverse v and v is equal to e raise to power minus x. Now derivative of sin theta is cos theta, therefore dy by du is equal to cos u. Now derivative of tan inverse x is 1 over 1 plus x square, therefore du by dv is equal to 1 over 1 plus v square and derivative of e raise to power x is e raise to power x into 1, therefore dv by dx is equal to minus 1 into e raise to power minus x. Hence dy by dx is equal to dy by du into du by dv into dv by dx. Now dy by du is cos u, so dy by dx is equal to cos u into du by dv is 1 over 1 plus v square into dv by dx is minus e raise to power minus x. Now substitute the value of u and v here, we get dy by dx is equal to cos u that is cos of tan inverse e raise to power minus x into 1 over 1 plus e raise to power minus 2x into minus e raise to power minus x. Hence the answer for the above question is minus e raise to power minus x cos of tan inverse e raise to power minus x upon 1 plus e raise to power minus 2x. I hope the solution is clear to you, bye and take care.