GATE | GATE 2017 MOCK II | Question 33

(A) tanx
(B) sec2x
(C) 2sinx
(D) 2cosx

Answer: (B)

Explanation: Expression Y can also be written as :
Y = \sqrt{tanx+y}
Squaring on the both sides,
=> y^2 - tanx -y=0
Derivate the above equation w.r.t. x,
=> 2y \frac{dy}{dx} - sec^2x - \frac{dy}{dx}=0
=> (2y-1) \frac{dy}{dx}=sec^x

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