Question

How do you take the derivative of `x = tan (x+y)`?

Answer 1

`(dy)/(dx)=-x^2/(1+x^2)`

Explanation:

I refer to http://socratic.org/questions/how-do-you-find-the-derivative-of-tan-x-y-x-1?answerSuccess=1, where we have found that given `x=tan(x-u)`; `(du)/(dx)=x^2/(1+x^2)` (I have replaced `y` by `u` for convenience). This means that if we substitute `u` by `-y`, we find that for `x=tan(x+y)`; `-(dy)/(dx)=x^2/(1+x^2)`, so `(dy)/(dx)=-x^2/(1+x^2)`.