The derivative of the function csc (5x) can be determined by following the trigonometric rule of differentiation. In this case, the derivative of csc x is -csc x cot x while that of 5x is 5. The total derivative and the answer to the problem asking for the is <span>derivative of csc(5x) is </span>-5 csc<span> 5x cot 5x. </span>