Question

Let y = t¹⁰ + 1 and x = t⁸ + 1, then `(d^2 y)/(dx^2)` to ______.

Options

• `5/2 t`

• 20t⁸

• `5/16t^6`

• None of these

Answer 1

Let y = t¹⁰ + 1 and x = t⁸ + 1, then `(d^2 y)/(dx^2)` to `bbunderline(5/16t^6)`.

Explanation:

y = t¹⁰ + 1, x = t⁸ + 1

⇒ `dy/dt = 10t^9, dx/dt = 8t^7`

⇒`dy/dx = (dy/dt)/(dx/dt)`

⇒ `(10t^9)/(8t^7) = 5/4t^2`

⇒ `(d^2y)/dx = 5/4(2t) dt/dx`

⇒ `5/4 × 2t × 1/(8t^7)`

⇒ `5/(16t^6)`