Question

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If y is a function of x and log (x+y) = 2xy, then the value of y'(0) =?

Answer 1

Given that y = f(x) 

Given that :-

log(x+y) = 2xy

Put x=0 in above equation to find y(0), we get :-

log(y) = 0

→ y(0) = 1  .......................(1)

Now differentiate the given equation with respect to x , we get :-

( 0 + y')/(x + y) = 2( 0 + xy')

→  y'/(x + y) = 2xy'

Now to find y'(0), put the value of x = 0 and y(0) = 1 in the above equation :-

 y'/(0 + 1) = 2 x 0 x 1

Thus, we get y'(0) = 0

I hope it helps.