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For a positive constant a find dy/dx,whe...

For a positive constant a find `dy/dx`,where`y = a^(t+(1/t)), and x = (t + 1/t)^a`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If x=ct, y = c/t, find dy/dx at t = 2

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  2. Find dy/dx, where x=t^3 + 1/t and y = (t+t^2)^3

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  3. For a positive constant a find dy/dx,wherey = a^(t+(1/t)), and x = (t ...

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  4. If (x=a sin (2t)(1+cos(2t)) and (y=b cos (2t) (1- cos(2t)), then show ...

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  5. If x = (1+logt)/t^2, y = (3+2logt)/t, t > 0, prove that y(dy/dx) - 2x(...

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  6. Find (dy)/(dx) in the following x = e^theta (sin theta + cos theta),...

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  7. Differentiate the following w.r.t. x: (sqrtx)^(sqrtx)

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  8. Differentiate the following w.r.t. x: (1/x)^x

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  9. Differentiate the following w.r.t. x: (x^x)^x

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  10. Differentiate the following w.r.t. x: x^(x^2)

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  11. Differentiate the following w.r.t. x: (5x)^(3cos2x)

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  12. Differentiate the following w.r.t. x: x^(sinx), x > 0

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  13. Differentiate the following w.r.t. x: (sin x)^x

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  14. Differentiate the following w.r.t. x: x^(sin^-1)

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  15. Differentiate the following w.r.t. x: x^x sin sqrtx

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  16. Differentiate the following w.r.t. x: (sinx)^(logx), sin x > 0

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  17. Differentiate the following w.r.t. x: (sinx)^(tanx)

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  18. Differentiate the following w.r.t. x: (sin x)^sinx

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  19. Differentiate the following w.r.t. x: (sec^2x)^(1//x)

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  20. Differentiate the following w.r.t. x: (x cos x)^x

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