# Dy/dx of ( ×²+2y+1) / (2x+4y+3)

2
by Sajith
form the question properly
here's the qn
please mention the question. is y = (x2 + 2y +1 ) / (2x + 4y +3) ?
say thanks pls

2014-07-27T22:45:23+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let  Z =    (x^2  + 2 y + 1 ) / (2 x + 4y +3)
d Z / d x  =  ?
Z ( 2x+4y+3) = x^2 + 2y +1
differentiate wrt x
Z (2 + 4 dy/dx ) + (2x+4y+3) dZ/dx = 2x + 2 dy/dx
dZ/dx (2x+4y+3)  = 2x - 2Z + (2 - 4Z) dy/dx
dZ/dx    =      1/(2x+4y+3)  [  2x  - 2Z +  2(1-2Z) dy/dx ]

2014-07-28T18:32:07+05:30
Y = ( x²+2y+1 ) / ( 2x+4y+3 )
dy/dx = ( 2x+4y+3 ) ( 2+2.dy/dx+0 ) - (x²+2y+1 ) (2+4.dy/dx+0 )
= (4x+4x.dy/dx+8y+8y.dy/dx+6+6.dy/dx) - (2x²+4x².dy/dx+4y+8y.dy/dx+2+4.dy/dx)
=(4x+8y+6-4x²-8y+4)dy/dx - 2x²+4x+4y+4
dy/dx(1+4x²-4x-10) = -2x²+4x+4y+4
dy/dx = -2x²+4x+4y+4/4x²-4x-9