If `y = x/(x+4)` then show that `x (dy)/(dx) = y(1-y)`

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If y=e^(x-y) then show that (dy)/(dx) = y/(1+y)

If y=(x)/(x+4) , Show that x(dy)/(dx)=y(1-y)

If Y = kx, then show that (dy)/(dx) = (y)/(x)

If y = e^(ax) Show that x(dy)/(dx) = y log y .

If e^x+e^y = e^(x+y) , show that (dy)/(dx) = -e^(y-x)

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

If log (x^(2)+y^(2)) = 2 tan ^(-1) (x/y) " then show that " (dy)/(dx) = (y-x)/(y +x)

If log (x^(2)+y^(2))=tan^(-1)((y)/(x)), then show that (dy)/(dx)=(x+y)/(x-y)

If y=sqrt(x)+(1)/sqrt(x) , then show that 2x(dy)/(dx)+y=2sqrt(x) .

If sin y=x sin(a+y), then show that: (dy)/(dx)=(sin a)/(1-2x cos a+x^(2))