 Hi and welcome to the session. I am Deepika here. Let's discuss the question. Find d over dx of the following function y is to power x is equal to x raise to power y So let's start the solution. Our given function is y raise to power x is equal to x raise to power y taking logarithm on both sides We get s log y is equal to y log x now differentiate both sides with respect to x We have We will apply product rule here on both the sides Now on the left hand side we have x into derivative of log y this is 1 by y and derivative of y with respect to x is dy by dx plus log y into 1 and on the right hand side we have y into derivative of log x that is 1 by x plus log x Into derivative of y with respect to x. So this is dy by dx now combining terms containing dy by dx We have we have two terms here. It is x by y and here it is log x So we get dy by dx into y y minus log x is equal to y by x minus log y So this implies dy by dx is equal to y by x minus log y upon x by y minus log x this implies dy by dx is equal to y by x into y minus x log y upon x minus y log x So we have found the dy by dx and our answer is dy by dx is equal to y by x into y minus x log y upon x minus y log x. I hope the question is clear to you. Why and enjoy yourself