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tan^(-1)((3x-x^(3))/(1-3x^(2)))...

`tan^(-1)((3x-x^(3))/(1-3x^(2)))`

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Verified by Experts

The correct Answer is:
`3/(1+x^(2))`
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Prove that tan^(-1)""(3a^(2)x-x^(3))/(a^(3)-3ax^(2))=3tan^(-1)""x/a .

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Derivative of tan^(-1)((x)/(sqrt( 1 - x^(2)))) with respect to sin^(-1) (3x - 4x^(3)) is

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(e) (SHORT ANSWER TYPE QUESTIONS)
  1. Differentiate the following w.r.t. x : xsec^(-1)x.

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  2. Differentiate the following w.r.t. x : cos^(-1)(sinx)

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  3. Differentiate the following w.r.t. x: (i)sin^(-1)2x" "(ii)tan^(-...

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  4. Differentiate the following w.r.t. x : (cot^(-1)x)^(2)

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  5. Differentiate the following w.r.t. x : sin(2sin^(-1)x)

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  6. Find the derivatives w.r.t. x : tan^(-1)((sinx)/(1+cosx))

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  7. "Tan"^(-1)(cosx)/(1+sinx)=

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  8. cot^(-1)((1+cosx)/(sinx))

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  9. Differentiate the following w.r.t. x : sin^(-1)(1-2x^(2))

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  10. sin^(-1)(3x-4x^(3))

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  11. Differentiate the following w.r.t. x : cos^(-1)(4x^(3)-3x),-1ltxlt1

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  12. Differentiate the following w.r.t. x : sin^(-1)((2x)/(1+x^(2))),-1lt...

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  13. "cosec"^(-1)((1+x^(2))/(2x))

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  14. Differentiate the following w.r.t. x : sin^(-1)((1-x^(2))/(1+x^(2)))...

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  15. Differentiate the following w.r.t. x : cos^(-1)((1-x^(2))/(1+x^(2)))...

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  16. Differentiate the following w.r.t. x : cos^(-1)((2x)/(1+x^(2))),-1lt...

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  17. Differentiate the following w.r.t. x : tan^(-1)((2x)/(1-x^(2))),0ltx...

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  18. tan^(-1)((3x-x^(3))/(1-3x^(2)))

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  19. निम्न फलन का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए - tan ^(-1) [(x^(1/...

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  20. "tan"^(-1)(x)/(sqrt(a^(2)-x^(2)))

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