If `e^y=y^x ,p rov et h a t(dy)/(dx)=((logy)^2)/(logy-1)`

If x^y= y^x , prove that (dy)/(dx)=((y/x-logy))/((x/y-logx))

If y^(x)=e^(y-x) , then prove that (dy)/(dx) = ((1+logy)^(2))/(logy)

Solve: x(dy)/(dx)=y(logy-logx-1)

x(dy)/(dx)=y(logy-logx+1)

Solve x(dy)/(dx)=y(logy-logx+1)

(dy)/(dx)+y/x logy=y/x^2 (logy)^2

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)

If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/(y^2)sqrt((1-y^6)/(1-x^6,) w h e r e-1x,1a n d-1

If x,=e^(cos2t) and y=e^(sin2t), prove that (dy)/(dx),=-(y log x)/(x log y)

y sqrt(1-x^(2))+x sqrt(1-y^(2))=1,prov et h a t (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))