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If y=(tan^(-1)x)^2, then (x^2+1)^2 (d^2y...

If `y=(tan^(-1)x)^2`, then `(x^2+1)^2 (d^2y)/(dx^2) + 2x(x^2+1) dy/dx=`

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4

B

2

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1

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TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. If y=log (log x) then (d^2y)/(dx^2) is equal to

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  2. The second order derivative of (e^x+1)/e^x is

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  3. If y=(tan^(-1)x)^2, then (x^2+1)^2 (d^2y)/(dx^2) + 2x(x^2+1) dy/dx=

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  4. If y=(sin^(-1)x)^(2),"show that "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)...

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  5. If y=(sin^-1x)^2/2,then(1-x^2)y2-xy1=

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  6. If sqrty=cos^-1x, then it satisfies the dIfferential equation (1-x^2)(...

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  7. If sqrtr=ae^(thetacotalpha), where a and alpha are real numbers, then ...

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  8. If y=2/sqrt(a^2-b^2)tan^-1[sqrt((a-b)/(a+b))tan(x/2)] then (d2y)/(dx^2...

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  9. If u = x^(2) + y^(2) " and " x = s + 3t, y = 2s - t , " then " (d^(2...

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  10. If x=at^2,y=2at, then (d^2x)/(dy^2)=

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  11. If x=f(t) and yy=g(t) are differentiable functions of t then (d^...

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  12. If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)

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  13. If x^2y^3=(x+y)^5, then (d^2y)/(dx^2) is

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  14. If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^...

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  15. If x=costheta, y=sin5theta then (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=

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  16. If y=e^sqrtx+e^(-sqrtx), then (x(d^2y)/(dx^2)+1/2.(dy)/(dx)) is equal ...

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

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  18. If x=acostheta,y=bsintheta , then (d^2y)/(dx^2) when theta=pi/4 is gi...

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  19. If y = x^(3)log ( log (1+x) ) ,theny''(0) =

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  20. If x=e^t sin t , y=e^t cos t, t is a parameter , then (d^2y)/(dx^2) at...

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