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Differentiate sin^(-1) ((1)/(sqrt(x + 1)...

Differentiate `sin^(-1) ((1)/(sqrt(x + 1)))`

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The correct Answer is:
`(-1)/(2 sqrtx (1 + x))`
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. Differentiate cos (tan sqrt(x+ 1))

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  2. Differentiate sin x^(2) + sin^(2)x + sin^(2) (x^(2))

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  3. Differentiate sin^(-1) ((1)/(sqrt(x + 1)))

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  4. Differentiate (sin x)^(cos x)

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  5. Differentiate sin^(m) x.cos^(n) x

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  6. Differentiate (x+1)^(2) (x + 2)^(3) (x + 3)^(4)

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  7. Differentiate cos^(-1) ((sin x + cos x)/(sqrt2)), - (pi)/(4) lt x lt (...

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  8. Differentiate tan^(-1) sqrt((1-cos x)/(1 + cos x)), - (pi)/(4) lt x lt...

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  9. Differentiate tan^(-1) (sec x + tan x), -(pi)/(2) lt x lt (pi)/(2)

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  10. Differentiate, tan^(-1) ((a cos x- b sin x)/(b cos x + a sin x)), (-pi...

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  11. Differentiate sec^(-1) ((1)/(4x^(3)-3x)), 0 lt x lt (1)/(sqrt2)

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  12. Write the following functions in the simplest form : tan^(-1)((3a^(2...

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  13. Prove that : tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-s...

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  14. Find (dy)/(dx): x=t + (1)/(t) and y= t - (1)/(t)

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  15. Find (dy)/(dx) of each of the functions expressed in parametric form: ...

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  16. Find (dy)/(dx) of each of the functions expressed in parametric form: ...

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  17. Find (dy)/(dx) of each of the functions expressed in parametric form: ...

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  18. Find (dy)/(dx) of each of the functions expressed in parametric form: ...

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  19. Find (dy)/(dx): x= e^(cos 2t) and y= e^(sin 2t) show that, (dy)/(dx)...

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  20. Find (dy)/(dx): x=a sin 2t (1+ cos 2t) and y= b cos 2t (1-cos 2t) ...

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