 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says find the derivative of 5xq plus 3x minus 1 into x minus 1. Let us start with a solution to this question. First of all let fx be equal to fxq plus 3x minus 1 multiplied by x minus 1. Let us open the bracket first of all. We have 5xq into x is 5 into x raised to power 4, 5xq into minus 1 is minus 5xq plus 3x into x is 3x square plus 3x into minus 1 is minus 3x, minus 1 into x is minus x, minus 1 into minus 1 is plus 1. This is same as 5 into x raised to power 4 minus 5xq plus 3x square, now minus 3x minus x is minus 4x plus 1. Now we find out f dash x that will be equal to 5 into 4 into x raised to power 4 minus 1, minus 5 into 3 into x raised to power 3 minus 1 plus 3 into 2 into x raised to power 2 minus 1 minus 4 into x raised to power 1 minus 1 plus 0. This happens because we see f dash x will be derivative of each term of fx added or subtracted. So for the first term we have 5x4 is 5 into 4 into x raise to power 4 minus 1 because d by dx of x raise to power n is equal to n into x raise to power n minus 1. In the first case n is 4 in the second n is 3 in the third n is 2 in the fourth n is 1 and since the last term is a constant so derivative of a constant is 0 so we get a 0 in the end. We have 5 4's are 20 x raise to power 3 minus 15 x square plus 6x minus 4. So our answer to this question is 20 x cube minus 15 x square plus 6x minus 4. I hope that you understood the question and enjoyed the session. Have a good day.