 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 and the function is x cube minus 27. So let us start with the solution to this question. Let us see what is the first principle according to first principle f dash x is equal to limit h approaching to 0 function at x plus h minus function at x divided by h. Now we have to find f dash x. So let us see what is fx. fx is the given function that is x cube minus 27. So function at x plus h will be we simply replace x by x plus h. So we will have x plus h the whole cube minus 27. Therefore f dash x will be limit h approaching to 0. Function at x plus h is x plus h the whole cube minus 27 minus function at x is x cube minus 27 divided by h. This will be equal to limit h approaching to 0. Now x plus h the whole cube is x cube plus 3 x square h plus 3 x h square plus h cube minus 27. Now this is minus x cube minus minus plus 27 the whole divided by h. Now we see that plus x cube gets cancelled with minus x cube minus 27 gets cancelled with plus 27 and we have limit h approaching to 0 3 x square h plus 3 x h square plus h cube divided by h. Now from these three terms we can take out h common. So we have limit h approaching to 0 h into 3 x square plus 3 x h plus h square divided by h. This h gets cancelled with this h. Now we simply put h equal to 0 in this expression and we get 3 x square plus 0 plus 0 and that is equal to 3 x square. So our answer to this question is 3 x square. I hope that you understood the question and enjoyed the session. Have a good day.