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myself yogesh from Faridabad if you don't mind would you please solve it

myself yogesh from Faridabad if you don't mind would you please solve it
 

Question Image
Grade:9

1 Answers

Vishal Kumar
26 Points
3 years ago
here since i am considering a as constant.
cos-1{ ( x2 – y) / ( x+ y2 ) } = log a
taking cos on both sides
 ( x2 – y) / ( x+ y2 ) = cos (log a)     
since cos(log a) is constant so consider it as k ( any constant )
( x2 – y) / ( x+ y2 ) = k       …..............1
a[pplying componendo and dividendo.
( 1 – k ) / ( 1+ k ) = y2 / x2      ..................2
from 1 
y2 = x2 *  { ( 1 – k ) / ( 1+ k ) }
now differintiating wrt x on bith sides
y * (dy/dx) =  x * { ( 1 – k ) / ( 1+ k ) }
dy/dx = (x/y) * { ( 1 – k ) / ( 1+ k ) }   ….....3
now putting 2 in 3
so dy/dx = (x/y) * (y2 / x2 )
hence dy/dx = y/x

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