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Find (d^2y)/(dx^2) , if x=a t^2,\ \ y=2a...

Find `(d^2y)/(dx^2)` , if `x=a t^2,\ \ y=2a t` .

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We have given
`x=a t^2,\ \ y=2a t`
On differentiating both sides w.r.t. t, we get,
`(dy)/(dt)=2at` and `(dy)/(dt)=2a`
Therefore,
`(dy)/(dx)=(2a)/(2at)=1/t`
`(d^2y)/(dx^2)=d/(dx)(1/t)`
`(d^2y)/(dx^2)=-1/(2at^3)`
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RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
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  2. If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

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  3. Find (d^2y)/(dx^2) , if x=a t^2,\ \ y=2a t .

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  10. If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...

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  11. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

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  14. Find second order derivative of x^3+tanx

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  15. Find second order derivative of sin(logx)

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  16. Find second order derivative of log(sinx)

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  17. Find second order derivative of e^xsin5x

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  18. Find second order derivative of e^(6x)cos3x

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  19. Find second order derivative of x^3logx

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  20. Find second order derivative of tan^(-1)x

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