Question

If x = at⁴, y = 2at², then `(dy)/(dx)` = ______. 

Options

• `1/t^2`

• t²

• 2t²

• `-1/t^2`

Answer 1

If x = at⁴, y = 2at², then `(dy)/(dx)` = `bbunderline(1/t^2)`.

Explanation:

Given: x = at⁴ and y = 2at²

To find: `(dy)/(dx)`

Step 1: Use the chain rule:

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

Step 2: Differentiate with respect to t:

`(dy)/(dt) = d/(dt)(2at^2) = 4at`

`(dx)/(dt) = d/(dt)(at^4) = 4at^3`

Step 3: Divide:

`(dy)/(dx) = (4at)/(4at^3) = 1/t^2`