Question

If e^y + x^y = e, then the value of d²y/dx² for x = 0 is

(A) 1/e

(B) 1/e²

(C) 1/e³

(D) none of these 

Answer 1

Answer is (B) 1/e²

When x = 0, e^y = e ⇒ y = 1

Differentiating w.r.t. x, we get

e^y(dy/dx) + y + x(dy/dx) = 0   .....(1)

e^y(d²y/dx²) + e^y(dy/dx)² + dy/dx + dy/dx + x(d²y/dx²) = 0   ....(2)

when x = 0, y = 1

∴ From (1)dy/dx = - 1/e

Putting the data in (2), we get

e.(d²y/dx²) + e.1/e² - 2/e = 0

∴ d²y/dx² = 1/e²