Find y' by implicit differentiation

Question

Find y' by implicit differentiation √(x+sec^2 y)=5

Answer 1

Rewrite the left side using rational exponents.

 

(x + sec²y)^1/2 = 5

 

 

Derive both sides of the equation using the chain rule.

 

(1/2)(x +sec²y)^-1/2(1 + 2secysecytany y') = 0

 

(1/2)(x + sec²y)^-1/2(1 + 2y'sec²ytany) = 0

 

[(y'sec²ytany) / √(x + sec²y)] = - [1 / 2√(x + sec²y)]

 

 

Next, multiply both sides of the equation by  [√(x + sec²y) / (sec²ytany)] to obtain the value of y'.