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If x=t^2,\ \ y=t^3 , then (d^2y)/(dx^2)=...

If `x=t^2,\ \ y=t^3` , then `(d^2y)/(dx^2)=` `(a)3//2` (b) `3//4t` (c) `3//2t` (d) `3t//2`

Text Solution

Verified by Experts

Correct option is B)
`x=t^{2} Rightarrow frac{dx}{dt}=2 t`
` y=t^{3} Rightarrow frac{dy}{dt}=3 t^{2}`
` Rightarrow frac{dy}{dx}=frac{3 t^{2}}{2 t}=frac{3}{2} t`
` therefore frac{d^{2} y}{dx^{2}}=frac{3}{2} times frac{dt}{dx}=frac{3}{2} times frac{1}{2 t}=frac{3}{4 t}`
`
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Knowledge Check

  • If x=tlogt,y=t^(t)," then "(d^2y)/(dx^(2))=

    A
    `logt`
    B
    `tx^(t-1)`
    C
    `e^(2)`
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    `3/(4t)`
    B
    `(3t)/4`
    C
    `4/(3t)`
    D
    `(4t)/3`

  • If x=2at^3,y=at^4 , then (d^2y)/(dx^2) at t=2 is

    A
    4
    B
    2a
    C
    `1/(2a)`
    D
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