 Hello and welcome to the session. I am Deepika here. Let's discuss the question. Differentiate the following function with respect to x. x is to power sin x plus sin x is to power cos x. So let's start the solution. Let y is our given function. y is equal to x is to power sin x plus sin x is to power cos x. Again put u is equal to x is to power sin x and v is equal to sin x is to power cos x. So then our y will become y is equal to u plus v. Differentiate both the sides with respect to x. We get on differentiating with respect to x both sides we get 1 by u into du by dx is equal to u's product rule here. Sin x into derivative of log x that is 1 by x plus log x into derivative of sin x this is cos x. So this implies du by dx is equal to u into sin x over x plus cos x log x. Now we have found du by dx similarly found fine we will find dv by dx. Now therefore now du by dx is equal to substitute the value of u here we get x is to power sin x into sin x over x plus cos x into log x. This is equal to sin x is to power cos x taking logarithm on both sides again method is same. We get log v is equal to cos x log of sin x. Now differentiate with respect to x using product rule we get 1 over v into dv by dx is equal to cos x into derivative of log of sin x. This is 1 over sin x into cos x plus log of sin x into derivative of cos x. This is minus sin x this implies dv by dx is equal to v into cos x into cos x minus sin x into log of sin x. Now substitute of value of v here we get therefore dv by dx is equal to sin x is to power cos x into cos x cot x minus sin x log of sin x. Now substitute values of du by dx and dv by dx in our equation 1 to get the value of dv by dx. We get dv by dx is equal to du by dx plus dv by dx. Now du by dx is x is to power sin x into sin x over x plus cos x log x plus dv by dx is sin x is to power cos x into cos x cot x minus sin x. log of sin x. Hence we have done the differentiation of our given function and our answer is x is to power sin x sin x over x plus cos x log x plus sin x is to power cos x into cos x cot x minus sin x log sin x. So this is our answer I hope the question is clear to you by and have a nice day.