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Differentiate w.r.t x : cot^-1{(sqrt (1+...

Differentiate w.r.t x : `cot^-1{(sqrt (1+sin x) + sqrt (1-sin x))/(sqrt (1+sin x) - sqrt (1-sin x))}, 0 < theta < pi/2`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following w.r.t. x: sin^-1(sqrt((1+x^2)/2))

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  2. If y = cot^-1{(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))}...

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  3. Differentiate w.r.t x : cot^-1{(sqrt (1+sin x) + sqrt (1-sin x))/(sqrt...

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  4. If y = tan^(-1)((5ax)/(a^2 - 6x^2)) . Prove that (dy)/(dx) = (3a)/(a^2...

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  5. If y = tan^-1 (4x)/(1+5x^2) + tan^-1(2+3x)/(3-2x), prove that dy/dx = ...

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  6. If f(x) = tan^-1x,g(x) = tan^-1((1+x)/(1-x)) fo |x| < 1, show that f' ...

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  7. If sqrt(1-x^6)+sqrt(1-y^6)=a^3(x^3-y^3), prove that : dy/dx = x^2/y^2s...

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  8. If y = tan^-1(cotx) + cot^-1(tanx), then prove that : dy/dx + 2 = 0

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  9. Differentiate : cos(2x+3)

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  10. Differentiate: cosx^2

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  11. Differentiate the following w.r.t. x: e^-x

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  12. Differentiate the following w.r.tx: e^(cot^-1x^2)

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  13. Differentiate the following w.r.tx: e^(mlogx)

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  14. Differentiate the following w.r.tx: sqrt(e^sqrtx), x > 0

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  15. Differentiate the following w.r.t x log(logx) , x > 1

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  16. Differentiate the following w.r.tx: log (sinx)

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  17. Differentiate the following w.r.t. x: log(cos e^x)

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  18. Differentiate the following w.r.t. x: sin(tan^-1 e^-x)

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  19. Differentiate the following w.r.tx: (cosx)/(logx), x>0

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  20. Differentiate the following w.r.tx: sqrt(tanx^0)alpha^x

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