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If x = (1+logt)/t^2, y = (3+2logt)/t, t ...

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

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following functions: cot^3 (2x+1) w.r.t.x^2 +1

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  2. Differentiate the following functions: x/(sinx) w.r.t sin x.

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

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  4. If x = 3 cos t - 2 cos^3 t and y = 3 sin t - 2 sin^3 t, show that dy/d...

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  5. Find dy/dx if x = (sin^3t)/(sqrtcos2t), y = (cos^3t)/(sqrtcos2t)

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  6. Find dy/dx if 3y = sqrt(sec^2 x -1)

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  7. Differentiate the following functions w.r.t.x sin^-1 3x

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  8. Differentiate the following functions w.r.t.x sin^-1 sqrtx

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  9. Differentiate the following functions w.r.t.x cos^-1(1-x)

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  10. Differentiate the following functions w.r.t.x sin^-1(cosx)

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  11. Differentiate the following functions w.r.t.x sin(tan^-1x)

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  12. Differentiate the following functions w.r.t.x (cot^-1x)^2

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  13. Differentiate the following functions w.r.t.x e^(sin^-1(x+1))

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  14. Differentiate the following functions w.r.t.x 1/sqrt2 cot ^-1 (sqrt2/x...

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  15. Differentiate the following functions w.r.t.x sqrt(sin^-1 2x)

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  16. Differentiate the following functions w.r.t.x x cos^-1sqrtx

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  17. Differentiate the following functions w.r.t.x tan(sin^-1x)

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  18. Differentiate the following functions w.r.t.x sec(tan^-1 x)

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  19. Differentiate the following functions w.r.t.x xtan^-1x

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  20. Differentiate the following functions w.r.t.x (sin^-1x)/x

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