 Hi and welcome to the session. I am Deepika here. Let's discuss the question. Differentiate the following with respect to x e to the power x plus e to the power x square plus so on plus e to the power x raise to power 5. So let's start the solution. Let y is equal to e raise to power x plus e raise to power x square plus so on till e raise to power x5. Differentiate with respect to x, we get dy by dx is equal to dy dx of e raise to power x plus dy dx of e raise to power x square plus dy dx of e raise to power x cube plus dy dx of e raise to power x4 plus dy dx of e raise to power x5. So dy by dx is equal to now derivative of e raise to power x with respect to x is e raise to power x. Now plus derivative of e raise to power x square with respect to x is e raise to power x square into dy dx of x square plus e raise to power x cube into dy dx of x cube plus e raise to power x4 into dy dx of x4 plus e raise to power x5 into dy dx of x raise to power 5. Therefore dy by dx is equal to e raise to power x plus 2x into e raise to power x square plus derivative of x cube is 3x square into e raise to power x cube plus 4x cube into e raise to power x4 plus 5x4 into e raise to power x5. So the answer for the above question is e raise to power x plus 2x into e raise to power x square plus 3x square into e raise to power x cube plus 4x cube into e raise to power x4 plus 5x4 into e raise to power x5. This is our answer. I hope the question is clear to you. Bye and have a nice day.