Question

If x = tan^-1t and y = t³ , find `(dy)/(dx)`.

Answer 1

x = tan^-1t and y = t³ 

∴ `(dx)/(dt) = 1/(1 + t^2)   "and"    (dy)/(dt) = 3t^2`

∴ `(dy)/(dx) = ((dy/dt))/((dx/dt)) = (3t^2)/(1/(1 + t^2))`

⇒ `(dy)/(dx) = 3t^2(1 + t^2)`