If x=e^ , y=e^ where is a parameter, then d y d x at (1,1) is equal to

Step-by-step solution

Given, x=c^ , y=c^ We have, d x d =c^0 +e^ and aligned & =c^ ( + ) d & =c^ (- )+c^ & =c^ ( - ) aligned On dividing Eq. (ii) by Eq (i), we get aligned d y d d x d & = e^ ( - ) e^ ( + ) & d y d x = (1- ) (1+ ) = 1- 1+ aligned As we also have, x y = e^ e^ x y = At (x, y)=(1,1) = 1 1 =1 Putting =1 into Eq. (iii), we get d y d x = 1-1 1+1 = 0 2 =0