Question

Find `(dy)/(dx)`, if x = 2at², y = at⁴.

Answer 1

x = 2at² 

Differentiating both sides w.r.t. t, we get

`(dx)/(dt)` = 4at

y = at⁴

Differentiating both sides w.r.t. t, we get

`(dy)/(dt) = 4at^3`

∴ `(dy)/(dx) = (((dy)/(dt)))/(((dx)/(dt))) = (4at^3)/(4at) = t^2`