If xy=ex-y,x>0, then the value of dydx at (1,1) is
0
12
1
2
Explanation for the correct option.
Step 1: Find dydx
The given equation is xy=ex-y
By taking log on the both sides, we get
ylogx=x-yloge⇒ylogx=x-yasloge=1
Differentiate with respect to x
logxdydx+y1x=1-dydx⇒logxdydx+dydx=1-yx⇒dydxlogx+1=x-yx⇒dydx=x-yx×1logx+1
Step 2: Find dydxat (1,1).
dydx1,1=1-11×1log1+1=0
Hence, option A is correct.