Question

If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.

विकल्प

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

If y = `x^((sinx)^(x^((sinx)^(x^...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to 1.00.

Explanation:

y = `x^((sinx)^y)`

⇒ ℓny = (sinx)^yℓnx

⇒ ℓny = `e^(yℓn(sinx)).ℓnx`

⇒ `1/y.(dy)/(dx) = 1/xe^(yℓn(sinx)) + ℓnx.e^(yℓn(sinx)) xx (y. 1/sinx . cosx + y^'ℓn(sinx))`

⇒ `1/y (dy)/(dx) = 1/(π/2) + 0`

⇒ `(dy)/(dx)` = 1

Since at x = `π/2`, y = `π/2`