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If y= (tan^(-1) x)^(2) show that (x^(2) ...

If `y= (tan^(-1) x)^(2)` show that `(x^(2) + 1)^(2) y_(2) + 2x (x^(2) + 1)y_(1) = 2`

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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Exercise-5.7
  1. If y= 500 e^(7x) + 600 e^(-7x), show that (d^(2)y)/(dx^(2))= 49y

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  2. If e^(y) (x+ 1)=1, show that (d^(2)y)/(dx^(2))= ((dy)/(dx))^(2)

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  3. If y= (tan^(-1) x)^(2) show that (x^(2) + 1)^(2) y(2) + 2x (x^(2) + 1...

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  4. Find the second order derivatives of the functions x^(2) + 3x+ 2

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  5. Find the second order derivatives of the functions x^(20)

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  6. Find the second order derivatives of the functions x.cos x

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  7. Find the second order derivatives of the functions log x

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  8. Find the second order derivatives of the functions x^(3) log x

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  9. Find the second order derivatives of the functions e^(x) sin 5x

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  10. Find the second order derivatives of the functions e^(6x) cos 3x

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  11. Find the second order derivatives of the functions tan^(-1)x

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  12. Find the second order derivatives of the functions log (log x)

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  13. Find the second order derivatives of the functions sin (log x)

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  14. If y=5 cos x-3 sin x, prove that (d^(2)y)/(dx^(2)) + y= 0

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  15. If y= cos^(-1)x, Find (d^(2)y)/(dx^(2)) in terms of y alone

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  16. If y= 3 cos (log x) + 4 sin (log x), show that x^(2)y(2) + xy(1) + y= ...

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  17. If y= Ae^(mx) + Be^(nx), show that (d^(2)y)/(dx^(2))- (m + n) (dy)/(dx...

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  18. If y= 500 e^(7x) + 600 e^(-7x), show that (d^(2)y)/(dx^(2))= 49y

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  19. If e^(y) (x+ 1)=1, show that (d^(2)y)/(dx^(2))= ((dy)/(dx))^(2)

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  20. If y= (tan^(-1) x)^(2) show that (x^(2) + 1)^(2) y(2) + 2x (x^(2) + 1...

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