If x = a( - ) and y = a(1 - ) , then (1 + y₁^2)^ 3/2 y₂ =

Step-by-step solution

Given x = a( - ) and y = a(1 - ) . Differentiating with respect to : dx d = a(1 - ) dy d = a Now, find the first derivative y₁ = dy dx : y₁ = dy d dx d = a a(1 - ) = 2 ( 2 ) ( 2 ) 2 ^2 ( 2 ) = ( 2 ) Next, find the second derivative y₂ = d^2y dx^2 : y₂ = d dx (y₁) = d d ( ( 2 ) ) d dx y₂ = - 1 2 ^2 ( 2 ) 1 a(1 - ) Since 1 - = 2 ^2 ( 2 ) : y₂ = - 1 2 ^2 ( 2 ) 1 2a ^2 ( 2 ) = - 1 4a ^4 ( 2 ) Now, evaluate the numerator (1 + y₁^2)^ 3/2 : (1 + y₁^2)^ 3/2 = (1 + ^2 ( 2 ) )^ 3/2 = ( ^2 ( 2 ) )^ 3/2 = ^3 ( 2 ) Finally, sub