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Prove that cos^-1x = pi/2 - sin^-1 x for...

Prove that `cos^-1x = pi/2 - sin^-1 x` for `-1lexle1` and use this result to find `d/dx(cos^-1x)`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following functions w.r.t.x sec^-1((x+1)/(x-1)) + si...

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  2. Differentiate the following functions w.r.t.x cos^-1((sinx+cosx)/sqrt2...

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  3. Prove that cos^-1x = pi/2 - sin^-1 x for -1lexle1 and use this result ...

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  4. Prove that sec^-1x = cos^-1(1/x) and use this to find d/dx (sec^-1x)

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  5. Prove that cot^-1x = pi/2 - tan^-1x and use this to find the derivativ...

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  6. Prove that tan(sin^-1 x) = (x/(sqrt 1-x^2)), 1 x 1 < 1

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  7. Find dy/dx if y = sin^-1x + sin^-1 sqrt(1-x^2), 0ltxlt1

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  8. Differentiate the following functions w.r.t.x x sin ^-1 x + sqrt(1-...

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  9. Differentiate the following functions w.r.t.x cot^-1((1+cosx)/(sinx...

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

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  11. Differentiate the following functions w.r.t.x: cot^-1 (cosec x + cot...

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  12. Differentiate the following functions w.r.t.x L 4 tan^-1(sqrt((1+cos...

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

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  14. Differentiate the following functions w.r.t.x L sec^-1 (1/(2x^2 -1))...

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

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

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  17. Differentiative the following (by suitable substitutions, if valid), w...

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  18. Differentiative the following (by suitable substitutions, if valid), w...

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  19. Differentiative the following (by suitable substitutions, if valid), w...

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  20. Differentiative the following (by suitable substitutions, if valid), w...

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