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If y = x^x, prove that y2 - y^-1 (y1)^2 ...

If `y = x^x`, prove that `y_2 - y^-1 (y_1)^2 - yx^-1 = 0`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find the second order derivative of the following functions If y = (...

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  2. If x = tan(1/a logy), then show that (1+X^2) (d^2y)/(dx^2) + (2x -a) d...

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  3. If y = x^x, prove that y2 - y^-1 (y1)^2 - yx^-1 = 0

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  4. If y = (tan^-1 x)^2, then prove that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^...

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  5. If y=[sin^-1 x]^2, then prove that : (1 -x^2) y2-xy1 - 2 = 0.

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  6. Find the second order derivative of the following functions If y = c...

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  7. If y = cosec^-1x,x>1, then show that : x(x^2-1)(d^2y)/(dx^2) + (2x^2-1...

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  8. If y = x^x, prove that y2 - y^-1 (y1)^2 - yx^-1 = 0

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  9. If y = e^(-ax) cos (bx + c), show that (d^2y)/(dx^2) + 2a(dy)/(dx) + ...

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  10. If y^2 = ax^2 + b, prove that (d^2y)/(dx^2) = ab/y^3

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  11. If x^2 + y^2 = a^2, prove that (d^2y)/(dx^2) = -a^2/y^3

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  12. If x^m y^n = (x+y)^(m+n), prove that dy/dx = y/x and (d^2y)/(dx^2) = 0

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  13. If x^2/a^2 + y^2/b^2 = 1, prove that (d^2y)/(dx^2) = -(b^4)/(a^2y^3)~

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  14. If sqrtx + sqrty = sqrtx , find (d^2y)/(dx^2) at x = a

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

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  16. Find (d^2y)/(dx^2) if x= cos theta, y = a sin theta)

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  17. If x = a sin^3 theta, y = a cos^3 theta, find (d^2y)/(dx^2) at theta ...

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  18. If x=a (cos t + t sin t) and y = a (sin t - t cos t ), find (d^2x)/(dt...

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  19. Find (d^2y)/(dx^2) in the following If x = a (theta + sin theta) , y...

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  20. If x=(1-t^2)/(1+t^2), y=(2t)/(1+t^2), find (dy)/(dx) at x=2.

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