Most Important Selected Qs for JEE AdvancedMathematicsDifferentiation

If y= x+ x+ x+ x+ , where x>0 , then d y d x can be:

Options

A1 2 y-1
Bx x+2 y
C1 1+4 x
Dy 2 x+y

Correct answer

D. y 2 x+y

Step-by-step solution

y= x+y y^2=x+y y^2-y-x=0 ...(1) (2 y-1) y^ =1 y^ = 1 2 y-1 (a) From equation (1), 2 y=1+ 1+4 x Hence, 2 y-1= 1+4 x y^ = 1 1+4 x (c) On dividing by y , equation (1) gives y-1= x y 2 y-2= 2 x y (d) : y 2 x+y = 1 2 x y +1 = 1 (2 y-2)+1 = 1 2 y-1 which is same as (a).

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