यदि ` y = x/( x+5)` , तो का मान ज्ञात कीजिए कि
` x dy/dx= y(1-y)`

Explanation

दिया है ` y = x/(x +5 )`
` (dy)/(dx) = (( x+5) .d/(dx) (x)-x.d/(dx)( x +5))/(( x +5)^(2)) = ((x+5).1-x.1)/((x+5)^(2))`
` = ( x+5-x)/(x+5)^(2) = 5/(x+5)^(2) rArr x (dy)/(dx) = (5x)/(x+5)^(2) " "`…(1)
तथा ` y ( 1-y) = x/( x +5) (1- x/(x+5)) = x/(x+5) (5/(x+5)) = (5x)/( x+5)^(2)" "`...(2)
अतः (1 ) और (2 ) से ,
` x (dy)/(dx) = y( 1-y)`.