If x (a+y)+ a (a+y)=0 , then d y d x is equal to

Step-by-step solution

Here, x (a+y)+ a (a+y)=0 ...(i) On differentiating w.r.t. x , we get aligned & d d x [x (a+y)]+ d d x [ a (a+y)]=0 & aligned [x d d x (a+y) . & .+ (a+y) d d x (x) ] & + a d d x (a+y)=0 aligned aligned (using product rule and chain rule) aligned & array r [x (a+y) d d x (a+y)+ (a+y) ] + a [- (a+y) d d x (a+y) ]=0 array & array r [x (a+y) (0+ d y d x )+ (a+y) ] - a (a+y) (0+ d y d x )=0 array & array r x (a+y) d y d x + (a+y) - a (a+y) d y d x =0 array aligned aligned & d y d x [x (a+y)- a (a+y)] &=- (a+y) & [ from E