 Hi and welcome to the session. I am Zitika here. Let's discuss the question, find dy by dx of the following function cos x raised to power y is equal to cos y raised to power x. So let's start the solution. Our given function is cos x raised to power y is equal to cos y raised to power x. So taking logarithm on both sides, we have log y log of cos x is equal to x log of cos y. Differentiate both the sides with respect to x. We have y into 1 over cos x into minus sin x plus log of cos x into derivative of y with respect to x is dy by dx. And on the right hand side again we will apply the product rule. x into derivative of log of cos y that is 1 over cos y into derivative of cos y minus sin y into derivative of this that is dy by dx. So plus log of cos y into 1, so this implies y minus y tan x plus log of cos x dy by dx is equal to minus x tan y dy by dx plus log of cos y. Now combining the terms containing dy by dx, so we have dy by dx into log of cos x plus x tan y is equal to log of cos y plus y tan x. So this implies dy by dx is equal to log of cos y plus y tan x upon log of cos x plus x tan y. Hence our answer for the above question is y tan x plus log of cos x plus x tan y. log of cos y upon x tan y plus log cos x. So I hope the question is clear to you. Bye and have a nice day.