 Hi, 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 x minus 2 raised to power sine x So let's start the solution that y is equal to Argument function that is x raised to power x minus 2 raised to power sine x Here we can't take direct logarithm on both sides as we don't have any formula for log of m minus n So we will proceed like this by putting u is equal to x is to power x and v is equal to 2 raised to power sine x we get y is equal to u minus v Therefore dy by dx is equal to du by dx minus dv by dx is equal to x raised to power x taking logarithm on both sides we get log u is equal to x log x Because log m raised to power n is equal to n log n log u is equal to therefore x log x Now differentiate both sides with respect to x we have 1 over u into du by dx is equal to x Here we use the product rule x into dy dx of log x plus log x into dy dx of x and this is equal to 1 by u into du by dx is equal to x into 1 by x plus log x This implies du by dx is equal to u into 1 plus log x and that is u is equal to x raised to power x this implies du by dx is equal to x raised to power x into 1 plus log x Now we want to find dv by dx and we will substitute in this equation the value of du by dx and dv by dx Let us give this as number 1 Now we have v is equal to power sine x taking logarithm on both sides we get log v is equal to sine x log 2 now differentiate Both sides with respect to x we have 1 over v into dv by dx is equal to now here use the product rule sine x into derivative of log 2 that is 0 plus log 2 into derivative of sine x that is cos x this implies dv by dx is equal to cos x log 2 into cos x log 2 Substitute a value of v here we get dv by dx is equal to 2 raised to power sine x into cos x log 2 Now we have du by dx is equal to x raised to power x into 1 plus log x and dv by dx is equal to 2 raised to power sine x into cos x log 2 substitute the value of du by dx and dv by dx In equation 1 to obtain the value of dv by dx we have dv by dx is equal to 6 to power x into 1 plus log x minus 2 raised to power sine x into cos x log 2 Hence we have differentiate our given function And the answer for the above question is x raised to power x into 1 plus log x minus 2 raised to power sine x into cos x log 2 I Hope the question is clear to you by a take care