The derivative of 5/x is equal to negative five divided by x squared. Using mathematical notation, the expression is written as d/dx 5/x = -5/x^2.
The derivative of 5/x can be determined by using the quotient rule. The quotient rule states that the derivative of y/x is equal to y times the derivative of x minus x times the derivative of y, all divided by x squared. For 5/x, the derivative is the derivative of five times x minus five times the derivative of x, all over x squared. The derivative of x is one, and the derivative of five is zero, resulting in negative five over x squared.