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Prove that derivative of tan^(-1)((x)/(1...

Prove that derivative of `tan^(-1)((x)/(1+sqrt(1-x^(2))))" w.r.t. "sin^(-1)x` is independent of x.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(h) (LONG ANSWER TYPE QUESTIONS (I))
  1. Differentiate w.r.t. as indicated : cos^(-1)(1/sqrt(1+x^(2)))" w.r.t...

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  2. Differentiate w.r.t. as indicated : sin^(-1)((2x)/(1+x^(2)))" w.r.t....

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  3. Differentiate w.r.t. as indicated : sin^(-1)((2x)/(1+x^(2)))" w.r.t....

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  4. Differentiate w.r.t. as indicated : "tan"^(-1)(3x-x^(3))/(1-3x^(2))"...

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  5. Differentiate cos^(-1)((1-x^(2))/(1+x^(2))) with respect to tan^(-1)((...

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  6. Differentiate w.r.t. as indicated : tan^(-1)((3x-x^(3))/(1-3x^(2)))"...

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  7. Differentiate w.r.t. as indicated : cos^(-1)((1-x^(2))/(1+x^(2)))" w...

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  8. Differentiate w.r.t. as indicated : tan^(-1)((sqrt(1+a^(2)x^(2))-1)/...

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  9. Differentiate w.r.t. as indicated : tan^(-1)((sqrt(1+x^(2))-1)/(x))"...

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  10. Differentiate w.r.t. as indicated : tan^(-1)(x/(sqrt(1-x^(2))))" w.r...

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  11. Differentiate w.r.t. as indicated : tan^(-1)(x/(1+sqrt(1-x^(2))))" w...

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  12. Write the derivative of e^x wrt. sqrtx

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  13. Differentiate w.r.t. as indicated : log(10)x" w.r.t. "x^(2)

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  14. Differentiate w.r.t. as indicated : sinx^(2)" w.r.t. "x^(3)

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  15. Differentiate w.r.t. as indicated : sqrt(1+x^(2))" w.r.t. "tan^(-1)x

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  16. Prove that derivative of tan^(-1)((x)/(1+sqrt(1-x^(2))))" w.r.t. "sin^...

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  17. Prove that the derivative of tan^(-1)((sqrt(1+x^(2))-1)/(x))" w.r.t. "...

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  18. Differentiate tan^(- 1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-...

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  19. Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x...

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  20. Differentiate tan^(-1)((sqrt(1+x^(2))+1)/(x))" w.r.t. "tan^(-1)((2xsqr...

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