 Hello and welcome to the session, I am Deepika here. Let's discuss the question, differentiate log x raised to power cos x with respect to x. So let's start the solution, solution that y is equal to log x raised to power cos x taking logarithm on both sides, on both sides we have log y is equal to cos x into log of log x. Now differentiating both sides with respect to x we have 1 over y dy by dx is equal to, right hand side we will differentiate by using the product rule that is u into derivative of v plus v into derivative of u. So this is equal to cos x into dy dx of log of log x plus log of log x into dy dx of cos x. So this is equal to 1 over y into dy by dx is equal to cos x into dy dx of log of log x is 1 over log x into dy dx of log x plus log of log x into derivative of cos x is minus sin x. This is equal to 1 over y dy by dx is equal to cos x into 1 over log x into 1 over x minus sin x into log of log x. Hence the differentiation of the above function is log x raised to power cos x into cos x upon x log x minus sin x log of log x. So this is our answer. I hope the question is clear to you. Bye and have a nice day.