 Hello friends, let's work out the following problem. It says find the derivative of the following function The given function is a plus b sine x upon c plus d cos x where a b c d are non-zero constants To find the derivative of this function will be using quotient rule Which is d by dx of u by v is equal to v into du by dx minus u into dv by dx upon v square So this will work as key idea Let us now move on to the solution We have to find the derivative of the function a plus b sine x upon c plus d cos x now for convenience Say u is equal to a plus b sine x and V is equal to c plus d cos x Now we'll find the derivative of this function by the quotient rule Which is v into du by dx minus u into dv by dx upon v square Let us now substitute the values of u and v in this v is c plus d cos x into d by dx of u that is a plus b sine x Minus u that is a plus b sine x into d by dx of v that is c plus d cos x upon v square that is c plus d cos x whole square Now this is equal to c plus d Cos x into the derivative of a plus b sine x now a and b are Constants so the derivative of a will be 0 so it becomes 0 plus and the derivative of v sine x is b cos x Because derivative of sine x is cos x and now this is a plus b Sine x into derivative of c plus d cos x now C and d are constants so derivative of c is 0 and derivative of d cos x will be minus d sine x because derivative of Cos x is minus sine x Upon c plus d cos x whole square Now this is equal to multiplying the two brackets becomes c b cos x plus b d cos square x minus a d sine x a into minus d sine x is a d sine x it is minus a d sine x and B into minus d sine x b sine x into minus d sine x is minus bd sine square x Upon e plus d cos x whole square now this is bc cos x plus bd cos square x Opening the brackets becomes plus a d sine x plus bd Sine square x upon c plus d cos x whole square Again this is equal to c b cos x plus a d sine x Taking bd common from these two terms We have bd into cos square x plus sine square x Upon c plus d cos x whole square Now this is again equal to c b cos x plus a d sine x plus Bd because we know that cos square x plus sine square x is 1 so bd into 1 is bd upon c plus d cos x whole square Hence the derivative of the given function is bc cos x Plus a d sine x plus bd upon c plus d cos x whole square and This completes the question by for now take care. Have a good day