Find dy/dx if y=tan^-1(a+x/1-ax)

Question

Tried solving this using the formula for d(tan^-1)/dx=1/(1+x^2), but was unsuccessful. I want to know how to solve this.

Answer 1

Use the Chain Rule: (Tan^-1u)' = [1 / (1+u²)] u', with u = (a+x) / (1-ax).

After taking the derivative and simplifying, we get [(1-ax)² / ((1+x²)(1+a²))] [ (1+a²)/(1-ax)²].

This simplifies to 1 / (1+x²).

Answer 2

URL to Desmos graph referenced in the video:

https://www.desmos.com/calculator/iuine9yqie