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1.If xy = 4 ,prove that x(dy/dx + y 2 ) =3y.. 2.If y=(e x - e -x /e x +e - x ),dy/dx=1-y 2 . 3.Ify=(x-1) log(x-1)-(x+1)log(x+1),prove that dy/dx=log(x-1/1+x).

1.If xy = 4 ,prove that x(dy/dx + y2) =3y..


2.If y=(ex - e -x/ex +e-x ),dy/dx=1-y2.


3.Ify=(x-1) log(x-1)-(x+1)log(x+1),prove that dy/dx=log(x-1/1+x).

Grade:

1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

1. y=4/x, thus dy/dx= -4/x2, x(dy/dx + y2) =x(-4/x2 + 16/x2) = 12/x=3y

2.from quotient rule, dy/dx = ((ex+e-x)(ex+e-x)-(ex-e-x)(ex-e-x))/(ex+e-x)2= 1-y2

3) from product rule, dy/dx= (x-1)/(x-1) + log(x-1) - (x+1)/(x+1) -log(x+1) = log((x-1)/(x+1))

 

 

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