If x13y7=x+y20 then xy'-y is.
7
13
20
0
Explanation for the correct option:
Finding the value of xy'-y:
Given,
x13y7=x+y20
On applying log on both sides
logx13y7=logx+y20⇒13logx+7logy=20logx+y[∵logab=loga+logb,andlogan=nloga]
On differentiating on both sides
13x+7yy'=20x+y1+y'⇒13x+7yy'=20x+y+20x+yy'⇒13x-20x+y=20x+yy'-7yy'⇒13x+13y-20xxx+y=y'20y-7x-7yx+yy⇒13y-7xx=y'13y-7xy⇒1x=y'y⇒xy'-y=0
Hence, the correct option is D.