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y=tan^(-1)((3x - x^3)/(1-3x^2), -1/sqrt3...

`y=tan^(-1)((3x - x^3)/(1-3x^2), -1/sqrt3

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Express the following functions in the simplest form : tan^-1(3x - x^3)/(1-3x^2), |x| < 1/sqrt3

Prove that : tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)), |x| < 1/sqrt3

Prove that 3 tan^-1 x = tan^-1(3x-x^3)/(1-3x^2), |x| < 1/sqrt3

Differentiate the following w.r.t. x: tan^-1((3x-x^3) / (1-3x^2)),-1/sqrt3 < x < 1/sqrt3

Draw the graph of y=tan^(-1)((3x-x^(3))/(1-3x^(2))) .

Differentiate tan^(-1) ((3x - x^3)/(1 - 3x^2)) w.r.t. tan^(-1)((2x)/(1 - x^2))

Prove that tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1

Prove that tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt(1)/(sqrt(3))

Evaluate the following integrals: int tan^(-1)((3x-x^3)/(1-3x^2))dx

Differentiate cos^(-1) ((1 - x^2)/(1 + x^2)) w.r.t. tan^(-1)((3x - x^3)/(1 - 3x^2))

PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Find dy/dx in the following: sin^2x + cos^2y = 1

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  2. Find dy/dx in the following: y=sin^-1(2x/(1+x^2)

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  3. y=tan^(-1)((3x - x^3)/(1-3x^2), -1/sqrt3<x<1/sqrt3 ਵਿੱਚ dy/dx ਪਤਾ ਕਰੋ।

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  4. y=cos^(-1)((1 - x^2)/(1+x^2), 0<x<1 ਵਿੱਚ dy/dx ਪਤਾ ਕਰੋ।

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  5. Find dy/dx in the following:y=sin^-1((1 - x^2)/(1+x^2), 0<x<1

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  6. Find dy/dx in the following: y=cos^-1((2x)/(1+x^2), -1<x<1

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  7. Find dy/dx in the following: y=sin^-1(2x sqrt(1-x^2)), -1/sqrt2ltxlt1/...

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  8. Find dy/dx in the following:y=sec^-1(1/(2x^2-1)), 0ltxlt1/sqrt2

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

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

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  11. Differentiate the following w.r.t. x: e^x^3

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

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

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  14. Differentiate the following w.r.t. x: e^x+e^(x^2)+. . . .+e^(x^5)

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

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  16. Differentiate the following w.r.t. x: log(log x), x>1

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  17. Differentiate the following w.r.t. x: cosx/logx, x>0

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  18. Differentiate the following w.r.t. x: cos(logx + e^x)

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  19. Differentiate the function w.r.t. x : cosx cdot cos2x cdot cos3x

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  20. Differentiate the function w.r.t. x : sqrt ((x-1)(x-2))/((x-3)(x-4)(...

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