 Hi and welcome to our session. Let us discuss the following question. The question says differentiate sine root x with respect to x from first principles. With the solution, let fx is equal to sine root x. We know that f dash x is equal to limit h approaches 0, h minus fx approaches 0 is equal to c minus t by 2, t by 2. By using this formula, we can write sine root x plus h minus sine root x by 2 divided by c squared. This can be written as cosine theta by theta.