If `x="tan"(y)/(2)+"log tan"(y)/(2)-2log(1+"tan"(y)/(2))`, show that,
`(dy)/(dx)=(1)/(2)"sin"(1+sin y+cos y)`

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

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

If tan y=(tan x+sec x-1)/(tan x-sec x+1), " show that, " (dy)/(dx)=(1)/(2) .

Find (dy)/(dx) , when y=log("tan"(x)/(2))

If y=(1)/(3)"log" (x+1)/(sqrt(x^(2)-x+1))+(1)/(sqrt(3))"tan"^(-1)(2x-1)/(sqrt(3)) , show that, (dy)/(dx)=(1)/(x^(3)+1)

If sin^(-1)x=tan^(-1)y , then show that, (1)/(x^2)-(1)/(y^2)=1 .

If x-sqrt(a^(2)-y^(2))=a" log"(a-sqrt(a^(2)-y^(2)))/(y) , show that, (dy)/(dx)=(y)/(sqrt(a^(2)-y^(2)))

If y=sinx log("tan"(x)/(2)) then the value of (d^(2)y)/(dx^(2))+y is -

If tan y = (tan x+sec x-1)/(tanx -sec x+1) show that (dy)/(dx) = 1/2

If y=a^(x^(a^(x^(…oo)))) , show that, (dy)/(dx)=(y^(2)logy)/(x(1-y log x log y)) .