Let y be an implicit function of x defined by

• Differentiation

Let y be an implicit function of x defined by x^2x - 2x^x cot y - 1 = 0. Then y′(1) equals

1. -1
2. 1
3. -log 2
4. log 2

Answer

When x = 1, y = π/2

(x^x – cot y)² = cosec² y

x^x = cot y + |cosec y|

When x = 1, y = π/2

⇒ x^x = cot y + cosec y

Differentiate w.r.t. to x

x^x(1 + ln x) = (-cosec² y - cosec y cot y)dy/dx

The correct option is A.