dy/dx of ( ײ+2y+1) / ( 2x+4y+3)
kvnmurty:
form the question properly
here's the qn
please mention the question. is y = (x2 + 2y +1 ) / (2x + 4y +3) ?
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Answers
Answered by
2
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 ]
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 ]
Answered by
1
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
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
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