find dy/dx by implicit differentiation

Question

a) tan(x-y)= y/(1+x^2)

b) tan^-1 (e^(-y) + e^(y))=x^2

Answer 1

Step 1:

(a) The function is .

Quotient Rule of derivatives: .

Apply derivative on each side with respect to .

Bring the terms containing on one side.

Solution :

.

Answer 2

Step 1:

(b) The function is .

Derivative formula:.

Apply derivative on each side with respect to .

Solution :

.