If x^a y^b=(x-y)^ a+b , then the value of d y d x - y x is equal to

Step-by-step solution

x^a y^b=(x-y)^ a+b taking log both the sides. aligned & (x^a y^b )= (x-y)^ (a+b) & a logx +b logy =(a+b) (x-y) & differentiating both sides w.r. ^ x^ . & a x + b y d y d x = (a+b) (x-y) [1- d y d x ] & d y d x [ b y + a+b x-y ]= a+b x-y - a x & d y d x [ b x-b y+a y+b y y(x-y) ]= a x+b x-a x+ x(x-y) & d y d x [ b x+a y y ]= b x+a y x & d y d x = y x & d y d x - y x =0 aligned