Differentiate y=a/x+b with respect to x, when a and b are constant​

-a/(x+b)²

Step-by-step explanation:

Given the function y = a/x+b

To differentiate, we will use the quotient rule.

dy/dx = (Vdu/dx-Udv/dx)/V²

Let u   = a

v = x+b

Note that differential of a constant is zero

du/dx = 0

dv/dx = 1

Substitute

dy/dx = (x+b)0 - a (1)/(x+b)²

dy/dx = 0 - a/(x+b)²

dy/dx = -a/(x+b)²