If `x^(y)=e^(x-y)`, then `dy//dx` is equal to which one of the following ?A. `((x-y))/((1+logx)^(2))`B. `(y)/((1+logx))`C. `((x+y))/((1+logx))`D. `((logx)/(1+logx)^(2))`

If `x^(y)=e^(x-y)`, then `dy//dx` is equal to which one of the followi

1.	If `x^(y)=e^(x-y)`, then `dy//dx` is equal to which one of the following ?A. `((x-y))/((1+logx)^(2))`B. `(y)/((1+logx))`C. `((x+y))/((1+logx))`D. `((logx)/(1+logx)^(2))`
Answer» Correct Answer - D `x^(y)=e^(x-y)` Taking log both sides, we get `rArr y.log x=x-y` `rArry=(x)/(1+logx)` `rArr(dy)/(dx)=((1+logx)-x(0+(1)/(x)))/((1+logx)^(2))` `=((1+logx)-1)/((1+logx)^(2))=(logx)/((1+logx)^(2))`