let `y=t^(10)+1,` and `x=t^8+1,` then `(d^2y)/(dx^2)` is

Options

A. `(5)/(2) t `
B. `20 t^(8)`
C. `(5)/(16 t^(6))`
D. None of these

Answer

B

Explanation

Given , ` y- 1 = t^(10) , " and " x - 1 = t^(8)`
` rArr (dy)/(dx) = 10 t^(9) " and " (dx)/(dy) = 8t^(7)`
`(dy)/(dx) = ((dy//dt)/(dx//dt)) = (10 t^(9))/(8t^(7)) = (5)/(4) t^(2)`
` rArr (d^(2) y)/(dx^(2)) = 5xx(2)/(4) = (10)/(4) t xx (1)/(8) = (5)/(16) t^(6)`