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If x^2 + y^2 = t -(1/t) and x^4 + y^4 = ...

If `x^2 + y^2 = t -(1/t)` and `x^4 + y^4 = t^2 + (1/ t^2)`, then show that `x^3 y (dy/dx) = 1`

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CHETANA PUBLICATION-Differentiation-Exercise
  1. Find dy/dx if: x= a(cos t + log tan (t/2)), y= a sin t

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  2. If x= sqrt (a^(sin^(-1) t)) and y= sqrt (a^(cos^(-1) t)), then show th...

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  3. If x^2 + y^2 = t -(1/t) and x^4 + y^4 = t^2 + (1/ t^2), then show that...

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  4. If x= e^t (sin t - cos t), y= e^t (sin t + cos t), find dy/dx at t= pi...

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  5. Differentiate tan^(-1) (log t) w.r.t. log(sec^(-1) t)

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  6. Differentiate log(sec x + tan x) w.r.t. x

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  7. If y= log x, then find (d^2y) / (dx^2)

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  8. If e^x + e^y = e^(x+y) , show that dy/dx = - e^(y-x)

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  9. Find (d^2 y)/(dx^2) of the following: y= x^3 + 5x^2 -7x + 10

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  10. Find (d^2 y)/(dx^2) of the following: y= log(frac{x^2}{e^x})

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  11. Find (d^2 y)/(dx^2) of the following: y= sin(log x)

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  12. Find (d^2 y)/(dx^2) of the following: y= x log x

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  13. If ax^2 + 2hxy + by^2 =0, show that dy/dx = y/x

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  14. Find (d^2 y)/(dx^2) of the following: x= sin sqrt t , y= sin sqrt t

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  15. Find (d^2 y)/(dx^2) of the following: x = a cos^3theta, y= b sin^3thet...

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  16. If x= costheta, y= sin^3theta, show that y(d^2 y)/(dx^2) + (dy/dx)^2 =...

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  17. If y= cos (m sin^(-1) x), show that (1- x^2)(d^2 y)/(dx^2) - x(dy/dx) ...

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  18. Find the nth derivative of the following: cos(5x+4)

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  19. Find the nth derivative of the following: 1/x

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  20. Find (d^2 y)/(dx^2) if y= x^2 + 3x +4

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