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Find dy/dx = -y/x if x = sqrt(a^(sin^-1t...

Find `dy/dx = -y/x` if `x = sqrt(a^(sin^-1t)), y = sqrt(a^(cos^-1t))`

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PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If x and y are connected parametrically by the equations given in Exer...

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  2. If x and y are connected parametrically by the equations given in Exer...

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  3. Find dy/dx = -y/x if x = sqrt(a^(sin^-1t)), y = sqrt(a^(cos^-1t))

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  4. Find the second order derivatives of the function : x^2+3x+2

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  5. Find the second order derivatives of the function: x^20

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  6. Find the second order derivatives of the function : x cdot cosx

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  7. Find the second order derivatives of the function : logx

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  8. Find the second order derivatives of the function : x^3logx

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  9. Find the second order derivatives of the function : e^x sin5x

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  10. Find the second order derivatives of the function : e^(6x )cos3x

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  11. Find the second order derivatives of the function : tan^-1x

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  12. Find the second order derivatives of the function : log(logx)

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  13. Find the second order derivatives of the function : sin(logx)

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  14. If y = 5cosx -3sinx prove that (d^2y/dx^2) + y = 0

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  15. If y = cos^-1x Find (d^2y/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 y2 + xy1 + y = 0

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  17. If y = Ae^(mx) + Be^(nx), Show that (d^2 /dx^2 y)-(m+n)dy/dx+mny = 0

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

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

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  20. If y=[tan^-1 x]^2, then prove that : (x^2 + 1)^2 y2+2x(x^2+1) y1 = 2.

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