derivative

Question

Given (x-y)+sec²(x+y)=tan²(x+y)+(x+y), find dy/dx in simplest form.

Answer 1

This problem has 2 methods of solution that I can see, one of which is to differentiate implicitily as the equation stands (hard) or simplify first and then differentiate implicitly (much easier).

 

If x-y + sec²(x+y) = tan²(x+y)+(x+y), then sec²(x+y)-tan²(x+y) = 2y

 

Recall the trig identity 1+tan²θ = sec²θ.  So, sec²θ - tan ²θ = 1

 

So, the original equation simplifies to 2y = 1

 

                                                       y = 1/2

 

Therefore, dy/dx = 0.