Question

If ln(x+y)=2xy, then y'(0)=

Answer 1

ln( x+y) = 2xy

differentiate

1/(x+y). ( 1+ y') = 2y + 2y'x

put x = 0

1/(y) .( 1+y') = 2y

put x= 0 in ln( x+y) = 2xy

ln( y) = 0

y= 1

So

(1+y') =2

y'(0) = 1

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