 Hello and welcome to the session. I am Deepika here. Let's discuss the question, differentiate the calling function with respect to x. Sin x raise to power x plus sin inverse root x. So let's start the solution. Let y is equal to a given function that is sin x raise to power x plus sin inverse root x. Put u is equal to sin x raise to power x and v is equal to sin inverse root x. So our y will become y. This implies y is equal to u plus v and dy by dx is equal to du by dx plus dv by dx. So let us give this as number one. Now consider u is equal to sin x raise to power x to find du by dx. Now our u was u is equal to sin x raise to power x. Method is same taking logarithm on both the sides. We get the log u is equal to x log sin x. Differentiate both the sides with respect to x using product rule. We will use product rule here. 1 by u into du by dx is equal to x into d by dx of log of sin x plus log of sin x into derivative of x. That is 1. This is equal to 1 by u into du by dx is equal to x into d by dx. Derivative of log of sin x. This is 1 over sin x because derivative of log x is 1 over x. So derivative of log of sin x is 1 over sin x into derivative of sin x which is cos x plus log of sin x. So this implies du by dx is equal to u into x cot x plus log of sin x. Substitute the value of u here we get du by dx is equal to sin x raise to power x into x cot x plus log of sin x. Now consider v is equal to sin inverse root x. Differentiating both the sides with respect to x, v by dx is equal to 1 over under root of 1 minus. Now sin inverse x is 1 over under root of 1 minus x. This is root x so this is 1 minus x into d by dx of root x. So this implies dv by dx is equal to into derivative of root x is 1 over 2 root x. Now substitute value of du by dx and dv by dx in equation 1. We get dy by dx is equal to du by dx which is equal to sin x raise to power x into x cot x plus log of sin x plus dv by dx. This is equal to 1 over root x into root 1 minus x. Hence we have finished with the differentiation and our answer is x raise to power x into x cot x 1 by 2 into root. So I hope the question is clear to you. Why and have a nice day.