 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 the following function from first principle x-1 into x-2. Let us see the solution to this question. First of all we see that according to first principle f dash x is equal to limit h approaching to zero function at x plus h minus function at x divided by h. So here we have to find out f dash x. First of all we find out function at x plus h for that. We see that function at x is given to be x minus 1 into x minus 2. So first of all we open the bracket here and we get x into x is x square. x into minus 2 is minus 2x minus x plus 2 and that is equal to x square minus 3x plus 2. Since this is function at x, so function at x plus h will be x plus h the whole square minus 3 into x plus h plus 2. Now what we have done here is we have simply replaced x by x plus h. This is equal to x square plus h square plus 2x h minus 3x minus 3h plus 2 that is equal to x square plus h square plus 2x h minus 3x minus 3h plus 2. We see that this remains as it is because there is no cancellation here. Now let us find out f dash x. So f dash x is limit h approaching to zero. Function at x plus h is x square plus h square plus 2x h minus 3x minus 3h plus 2 minus fx will be minus x square plus 3x minus 2 this divided by h. This is equal to limit h approaching to zero. Now we see that plus x square gets cancelled with minus x square minus 3x gets cancelled with plus 3x plus 2 gets cancelled with minus 2 and we have h square plus 2x h minus 3h divided by h. Now taking out h common from these three terms we have limit h approaching to zero h into h plus 2x minus 3 divided by h. Now we see that h gets cancelled with h and we have h plus 2x minus 3. Now if we put h equal to zero applying the limits we get 2x minus 3. So our answer to this question is 2x minus 3. I hope that you understood the question and enjoyed the session. Have a good day.