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If y = x^y, prove that (dy)/(dx) = (y^2)...

If `y = x^y`, prove that `(dy)/(dx) = (y^2)/(x(1 - y log x))`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If y = sqrt(x+ sqrt(x + sqrt(x + ......oo))), show that (2y - 1) (dy)/...

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  2. If y = sqrt(3^x+sqrt(3^x+sqrt(3^x+….......oo))), then prove that : (2y...

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  3. If y = x^y, prove that (dy)/(dx) = (y^2)/(x(1 - y log x))

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  4. If y = (cosx)^(cosx^(cosx……..to infty)) prove that dy/dx = (-y^2 tanx)...

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  5. If y=(tanx)^((tanx)^((tanx)^...oo)), then prove that (dy)/(dx)=2 at x=...

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  6. If y = (x^(x^(x)….......to oo)), prove that xdy/dx=y^2/(1-ylogx).

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  7. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : 1+2x

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  8. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : ax^3...

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  9. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : 1/(2...

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  10. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : log ...

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  11. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : e^x ...

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  12. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : e^x ...

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  13. Find the second derivative of the following functions: x^20

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  14. Find the second derivative of the following functions: x^2 + 3x +2

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  15. Find the second order derivative of the function x.cosx

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  16. Find the second derivative of the following functions: x^3 + tanx

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  17. Find the second derivative of the following functions: tan^-1x

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  18. Find the second derivative of the following functions: logx

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  19. Find the second order derivative of the following functions x^3 log ...

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  20. Find the second derivative of the following functions: log(logx)

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