 Hi and welcome to the session. I am Deepika here. Let's discuss the question. Find the derivative of the function given by fx is equal to 1 plus x into 1 plus x square into 1 plus x4 into 1 plus x is to power 8 and hence find f dash 1. So let's start the solution. Let y is our given function. y is equal to 1 plus x into 1 plus x square into 1 plus x is to power 4 into 1 plus x is to power 8. So taking logarithm on both sides, log y is equal to log of 1 plus x plus log 1 plus x square plus log 1 plus x is to power 4 plus log 1 plus x is to power 8. Differentiate both the sides with respect to x. Derivative of log y that is 1 by y into derivative of y with respect to x that is dy by dx. Now derivative of log of 1 plus x this is 1 over 1 plus x plus 1 over 1 plus x square into derivative of x square that is 2x plus 1 over 1 plus x is to power 4 into derivative of x4 4x cube plus 1 over 1 plus x is to power 8 into derivative of x8 that is 8x is to power 7. So this implies f dash x is equal to dy by dx is equal to y into 1 over 1 plus x plus 2x over 1 plus x square plus 4x cube over 1 plus x is to power 4 plus 8x 7 over 1 plus x is to power 8. Substitute value of y here we get f dash x is equal to 1 plus x into 1 plus x square into 1 plus x is to power 4 into 1 plus x is to power 8 into 1 over 1 plus x plus 2x over 1 plus x square plus 4x cube over 1 plus x4 plus 8x 7 over 1 plus x is to power 8. Now f dash 1 is equal to substitute the value x is equal to 1 in this derivative we get f dash 1 is equal to 1 plus 1 this is 2 into 1 plus 1 square that is again 2 into 1 plus 1 is to power 4 which is same 2 into 1 plus 1 is to power 8 2 into 1 over 1 plus 1 2 plus 2 over 1 plus 1 2 plus 4 over 2 plus 8 over 2 therefore f dash 1 is equal to 16 into 15 by 2 so this is equal to f dash 1 is equal to 120 hence our answer for the given question is derivative of the given function is 1 plus x into 1 plus x square into 1 plus x is to power 4 into 1 plus x is to power 8 into 1 over 1 plus x plus 2x over 1 plus x square plus 4x cube over 1 plus x is to power 4 plus 8x 7 over 1 plus x 8 and f dash 1 is equal to 120 so this is our answer I hope the question is clear to you by and enjoy yourself