 Hello and welcome to the session, I am Deepika here. Let's discuss the question differentiate the following with respect to x log of cos e raised to power x. So let's start the solution. Here we will use a chain rule that y is equal to log u where u is equal to cos v and v is equal to e raised to power x. Therefore dy by du is equal to now derivative of log x is 1 over x. Therefore derivative of log u is 1 over u. Now derivative of cos x is minus sin x. Therefore du by dv is equal to minus sin v and dv by dx is equal to e raised to power x. Therefore dy by dx is equal to dy by du into du by dv into dv by dx. Now dy by du is 1 over u into du by dv is minus sin v into dv by dx is e raised to power x. Now substitute the value of u and v here we get dy by dx is equal to 1 over cos e raised to power x into minus sin e raised to power x into e raised to power x and this is equal to minus e raised to power x into tan e raised to power x. Now tan x is equal to 0 when x is equal to 2n plus 1 pi by 2. So therefore e raised to power x should not be equal to 2n plus 1 pi by 2 where n belongs to n. Hence the answer for the above question is, hence the derivative of the above function is minus e raised to power x into tan e raised to power x where e raised to power x is not equal to 2n plus 1 pi by 2 where n belongs to n. Hence this is our answer. I hope the solution is great to you. Bye and take care.