 Hi, and welcome to your session. Where is this task of all in question? The question says differentiate sine 2x plus 3 with respect to x from first principle. Let's now begin with the solution, let fx is equal to sine 2x plus 3. We know that f dash x is equal to limit h approaches 0, f of x plus h minus f of x divided by h. f dash x, we will first need to find f of x plus h. Now, f of x plus h is equal to sine 2 into x plus h plus 3. And this is equal to sine 2x plus 2h plus 3. Now, f dash x is equal to limit h approaches 0, f of x plus h minus f of x divided by h. Now, f of x plus h is, we know that sine minus d by, now by using this formula, this numerator is equal to plus 2h plus 3 minus 2x minus 3 divided by 2 is also equal to 1. So we have 2 into 1. Limit h approaches 0, cos 4x plus 2h plus 6 divided by 2 is x divided by.