If ( x+y x-y )= 5 , then d y d x =

Step-by-step solution

Given ( x+y x-y )= 5 x+y x-y = ⁻¹ ( 5 ) x+y x-y =K say ...(1) x+y=K(x-y) 1+ d y d x =K (1- d y d x ) 1+ d y d x =K-K d y d x (1+K) d y d x =K-1 d y d x = K-1 K+1 aligned d y d x &= x+y x-y -1 x+y x-y +1 [ From (1) ] &= x+y-x+y x+y+x-y = 2 y 2 x = y x aligned This problem can also be solved as follow: x+y x-y = ⁻¹ ( 5 ) Differentiating w.r.t. x , we get aligned & (x-y) (1+ d y d x )-(x+y) (1- d y d x ) (x-y)² =0 & (x-y+x d y d x -y d y d x )- (x+y-x d y d x -y d y d x )=0 &-2 y+2 x d y d x =0 d y d x = y x aligned