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Find the derivative of y=e^(Sin-1)x....

Find the derivative of `y=e^(Sin-1)x`.

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The correct Answer is:
`(e ^(sin ^(-1) x ))/( sqrt (1- x ^(2)))`
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AAKASH SERIES-DIFFERENTIATION -EXERCISE -4.4
  1. Find the derivatives of the function cos ec ^(-1) (e ^(2x +1))

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  2. Find the derivatives of the function cot ^(-1) (cosec 3x )

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  3. Find the derivative of y=e^(Sin-1)x.

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  4. Find the derivatives of the function sin ^(-1) sqrtx

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  5. Find the derivatives of the function tan ^(-1) (cos sqrtx)

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  6. Find the derivatives of the function sin (tan ^(-1) (e ^(x)))

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  7. Find the derivatives of the function (cot ^(-1) x ^(3)) ^(2)

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  8. Find the derivatives of the function tan ^(-1) (( cos x )/( 1 + cos ...

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  9. Find the derivatives of the function cos ^(-1) (( b + a cos x )/( a ...

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  10. Find the derivatives of the function log (sin ^(-1) e ^(x))

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  11. Find the derivatives of the function If y = b tan ^(-1)((x )/(a) + ...

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  12. Find the derivative of the function If f(x) = tan ^(-1) ((5 tan ((x...

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  13. Find the derivatives of the function x tan ^(-1) x

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  14. Find the derivative of the function sin x (tan ^(-1) x) ^(2)

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  15. Find the derivative of the function sin ^(2) x (sin ^(-1) x ) ^(2)

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  16. Find the derivatives of the function (x sin ^(-1) x )/( sqrt (1 - x ^...

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  17. Find the derivatives of the function If x = log (1 + sin ^(2)y ) show...

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  18. If x=tan(e^(-y)), then show that (dy)/(dx)=(-e^y)/(1+x^2).

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  19. Find the derivatives of the function If x = log (1 + sqrty), then sh...

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  20. If y = e^(asin^(-1)x) then prove that (dy)/(dx) = (ay)/(sqrt(1 - x^2))

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