Question

Differentiate it by using the first principle. Refer to the picture below.

Answer 1

The function is given as

$f(x)=\frac{ax}{x-1}$

Differentiate the function

$f^{\prime}(x)=\frac{a(x-1)-ax}{(x-1)^2}=-\frac{a}{(x-1)^2}$

Hence the answer is

$\frac{a}{(x-1)^2}$