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let y=t^(10)+1, and x=t^8+1, then (d^2y)...

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

A

`(5)/(2)t`

B

`20t^(8)`

C

`(5)/(16t^(6))`

D

none of these

Text Solution

Verified by Experts

`"Here, "y=t^(10)+1 and x=t^(8) +1`
`therefore" "t^(8)=x-1 or t^(2)=(x-1)^(1//4)`
`"So, "y=(x-1)^(5//4)+1`
Differentiating both sides w.r.t. x, we get `(dy)/(dx)=(5)/(4)(x-1)^(1//4)`
Again, differentiating both sides w.r.t. x, we get
`(d^(2)y)/(dx^(2))=(5)/(16)(x-1)^(-3//4)=(5)/(16(x-1)^(3//4))=(5)/(16(t^(2))^(3))=(5)/(16t^(6))`
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