 Hi and welcome to our session. Let us discuss the following question. The question says differentiate tan root x with respect to x from post-principles. Let us now begin the dissolution. Let fx is equal to tan root x. h is equal to x plus h. Note that f dash x is equal to limit h approaches 0 plus fx divided by 2 sin a minus b divided by cos a cos b. By using this formula, we can write the numerator plus root x. We have used the identity of a squared minus b squared minus root x divided by root x plus h minus root x is equal to 1. Limit h approaches 0 by root x plus h plus root x is cos root x plus h into cos root x is...