 Hello and welcome to the session, I am Deepika here. Let's discuss the question, point d by dx of the following function, x is to power y plus y raise to power x is equal to 1. So let's start the solution. Given that x is to power y plus y raise to power x is equal to 1, now putting u is equal to x raise to power y and v is equal to y raise to power x, we get u plus v is equal to 1. Now differentiate both sides with respect to x, d u by dx plus d v by dx is equal to 0. So let us take this as equation number 1. Now find the derivative of u and derivative of v and we will substitute in equation 1. Now consider u is equal to x raise to power y taking logarithm on both the sides, we have log u is equal to y log x. Now differentiate both sides with respect to x, we have 1 by u into d u by dx is equal to, now we will find derivative of y log x using product rule. So y into derivative of log x that is 1 by x plus log x into derivative of y with respect to x this is d y by dx this implies d u by dx is equal to u into y by x plus log x into d y by dx. Substitute the value of u here, we get d u by dx is equal to x raise to power y into y by x plus log x into d y by dx so we have d u by dx is equal to d u by dx is equal to y into x raise to power y minus 1 plus x raise to power y into log x d y by dx now we will find out d v by dx so again we have v is equal to y raise to power x this implies taking log on both sides we get log v is equal to x log y. Now differentiate both sides with respect to x we get 1 by v into d v by dx is equal to x into derivative of log y this is 1 over y into derivative of y with respect to x is d y by dx plus log y into derivative of x that is 1 so this implies d v by dx is equal to v into x by y d y by dx plus log y now substitute the value of v here we get d v by dx is equal to v raise to power x into x raise to power y x by y d y by dx plus log y which is equal to into y raise to power x minus 1 d y by dx plus y raise to power x into log y now substitute values of d u by dx and d v by dx in equation 1 we have y into d u by dx is y into y into x raise to power y minus 1 plus x raise to power y log x d y by dx plus d v by dx is x y raise to power x minus 1 d y by dx plus y raise to power x log y is equal to 0 now collect the term containing d y by dx we have d y by dx into x raise to power y log x plus x y raise to power x minus 1 is equal to minus y x minus 1 minus y raise to power x log y so this implies d y by dx is equal to minus y raise to power y minus 1 minus y raise to power x log y upon x raise to power log x plus x y raise to power x minus 1 hence the answer for the above question is d y by dx is equal to minus minus 9 common y x raise to power y minus 1 plus y raise to power x log y upon x y raise to power x raise to power y log x plus x into y raise to power x minus 1 this is our answer given question I hope the question is clear to you my and have a nice day