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