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Find the derivatives of the following fu...

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

Text Solution

Verified by Experts

The correct Answer is:
`(e^(x))/(sin^(-1)(e^(x))sqrt(l-(e^(2))^(x)))`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIATION-Exercise-9(b)
  1. Find the derivatives of the function tan ^(-1) (log x)

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  2. Find the derivative of log((x^(2)+x+2)/(x^(2)-x+2)) w.r.to x.

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

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

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  5. Find the derivative of y=(cosx)/(sinx+cosx).

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  6. Find the derivatives of the following function. (x(l+x^(2)))/(sqrt(l...

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

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  8. Find the derivatives of the following function. y=cos(logx+e^(x))

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  9. Find the derivatives of the following function. y=(sin(x+a))/(cosx)

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

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  11. Find the derivatives of the following functions. x=sinh^(2)y

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  12. Find the derivatives of the following functions. x=tanh^(2)y

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  13. Find the derivatives of the following functions. x=e^(sinh y)

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  14. Find the derivatives of the following functions. x=tan(e^(-y))

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

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

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  17. Find the derivative of v = cos [log(cotx)]

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  18. Find derivative y=sinh^(-1)((1-x)/(1+x)).

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  19. Find the derivative of w.r.to x log (cot ( 1 - x ^(2)))

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  20. Find the derivatives of the following functions. y=sin[cos (x^(2))]

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