Question

Find dy/dx if x=at⁴, y = at³
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Answer 1

The answer for dy/dx is 3/4t .

Explanation:

First, you have to differentiate x and y expressions in term of t :

`x = a {t}^(4)`

`(dx)/(dt) = 4a {t}^(3)`

`y = a {t}^(3)`

`(dy)/(dt) = 3a {t}^(2)`

Next, we can assume that dy/dt ÷ dx/dt = dy/dx. So we have to substitute the expressions :

`(dy)/(dt) / (dx)/(dt) = (dy)/(dt) * (dt)/(dx) = (dy)/(dx)`

`(dy)/(dx) = 3a {t}^(2) / 4a {t}^(3)`

`(dy)/(dx) = 3a {t}^(2) * \frac{1}{4a {t}^(3) }`

`(dy)/(dx) = (3)/(4t)`