Inverse trigonometric Derivative problems and solutions

In differential calculus, we are able to differentiate the inverse trigonometric functions once we learn the derivative rules of inverse trigonometric functions. Here is the list of differentiation problems of inverse trigonometric functions with solutions, if you already learnt the differentiation formulas of inverse trigonometric functions.

Evaluate $\dfrac{d}{dx}{\Bigg[\dfrac{1}{b}\tan^{-1}{\Big(\dfrac{x}{b}\Big)}-\dfrac{1}{a}\tan^{-1}{\Big(\dfrac{x}{a}\Big)}\Bigg]}$