 Hello and welcome to the session, my name is Asha and I am going to help you with the following question that says, find the derivative of the following functions from the first principle. Let us now start with the solution and let us denote the given function by f x, so f x is equal to cos x minus pi upon 8. Therefore, f at x plus h is equal to cos x plus h minus pi upon 8. Now, here f is a real valued function, so it is derivative but the help of first principle is given by limit as h approaches to 0, f at x plus h minus fx upon h and wherever the limit exists, this is defined as the derivative of f at the point x and is denoted by f dash x. This is further equal to limit as h approaches to 0 cos x plus h minus pi by 8 minus cos x minus pi by 8 upon h. Now, cos x minus cos y is given by minus 2 sin x plus y upon 2 into sin x minus y upon 2, so this limit can further be written as limit as h approaches to 0 minus 2 sin on adding x plus h minus pi upon 8 and x minus pi upon 8 we get x plus h minus pi by 4 upon 2 into sin. Now, on subtracting x minus pi upon 8 from x plus h minus pi upon 8 we get h, the denominator we have to upon h. This is further equal to limit as h approaches to 0 sin x plus h upon 2 minus pi upon 8 into sin h by 2 upon h by 2 taking this 2 in the denominator and this negative sign. Now, this is further equal to limit as h approaches to 0 sin x plus h upon 2 minus pi upon 8, negative sign also into limit as h approaches to 0 sin h upon 2 upon h upon 2. This is further equal to limit as h approaches to 0 minus sin x plus h upon 2 minus pi upon 8 and limit of this function is equal to 1 since if h approaches to 0 this implies that h upon 2 also approaches to 0 and limit as h upon 2 approaches to 0 sin h upon 2 upon h upon 2 is equal to 1 and so we further have minus limit as h approaches to 0 sin x minus pi upon 8 plus h by 2. Now as limit h approaches to 0 the value of this term is equal to 0 and this further implies we have minus sin x minus pi by 8. Thus our answer is the derivative of course x minus pi by 8 is minus sin x minus pi by 8 with the help of first principle. So, this complete specification hope you have understood it take care and have a good day.