 Hello and welcome to the session, I am Deepika here. Let's discuss the question, differentiate the following with respect to x, cos of log x plus e to the power x, x is greater than 0. So let's start the solution, that y is equal to cos t, where t is equal to log x plus e to the power x. Here dy by gt, differentiate with respect to t, we get dy by gt is equal to minus sin t and differentiate this with respect to x, we get dt by dx is equal to 1 over x plus e to the power x. Now by chain rule we have dy by dx is equal to dy by gt into dt by dx. So this is equal to dy by dt is minus sin t into dt by dx is 1 over x plus e to the power x. Hence dy by dx is equal to minus sin t into 1 over x plus e to the power x. Now substitute the value of t here, so dy by dx is equal to minus sin log x plus e to the power x into 1 over x plus e to the power x and our x is greater than 0. Hence we have differentiated our given function and our answer is minus 1 over x plus e to the power x into sin log x plus e to the power x, x is greater than 0. I hope the question is clear to you, why and have a nice day.