Question

(36. If ex+ ey = ex+y, then what is value of
dy/dx at point (1,
1)?
(a) o
(c) 1
(b) -1
(d) None of these​

Answer 1

Answer:

→ choose ans. (b) -1

Step-by-step explanation:

e^x+ e^y = e^(x+y)

e^x+ y'e^y = (1 + y')e^(x+y) = e^(x+y) + y'e^(x+y)

y'{e^(x+y) - e^y} =  e^x - e^(x+y) = e^x ( 1- e^y)

y'e^y{e^x - 1} = e^x ( 1- e^y)

y' = e^x ( 1 - e^y) ÷ e^y{e^x - 1}

y' = e^(x -y) {( 1 - e^y) ÷ {e^x - 1} }

at (1,1)

y' = e^0{1-e ÷ e-1} = -1

→ choose ans. (b) -1