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Differentiate the following w.r.t. x : ...

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

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The correct Answer is:
`(e ^(-x) cos (tan ^(-1) e ^(-x)))/( 1 + e ^(-2x))`
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AAKASH SERIES-DIFFERENTIATION -EXERCISE -4.6 (SHORT TYPE ANSWER QUESTIONS )
  1. Find the derivative of the w.r.t.x (x cos x )/( sqrt (1+ x ^(2)))

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  2. Find the derivative of the w.r.t.x (x (1+ x ^(2)))/( sqrt (1- x ^(2)...

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  3. Find the derivative of the w.r.t.x (1- cos 2x)/( 1 + cos 2x)

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  4. Find the derivative of the w.r.t.x log [(sin (log x ) + x log x log ...

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  5. Find the derivative of the w.r.t.x sqrt (cos sqrtx)

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  6. Find the derivative of the w.r.t.x log (( sqrt (e ^(x) +1 )-1)/( sqr...

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

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

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  9. Differentiate the following w.r.t. x : (cos x)/(log x), x gt 0.

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  10. Tan ^(-1) ((1 - x )/( 1 +x ))

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  11. Tan ^(-1) (sqrt((1- x )/( 1 +x ))) (where |x| lt 1)

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  12. Find the derivative of Tan^(-1) sqrt((1-cos x)/(1+cos x))

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  13. Tan ^(-1) (sqrt ((1 - sin x )/( 1 + sin x )))

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  14. Tan ^(-1) ((a -x)/( 1 + ax) )

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  15. If y = Tan^(-1)((3a^2x-x^3)/(a^3-3ax^2))then (dy)/(dx)=

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  16. Tan ^(-1) ((4x - 4x ^(3))/(1 - 6x ^(2) + x ^(4)))

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  17. Differentaite Tan ^(-1) ((x - sqrtx)/(1 + x sqrtx))

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  18. Find the derivative of Tan ^(-1) (( sqrt (1 + x ) - sqrt ( 1 -x ))/( s...

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  19. d/dx{Tan ^(-1) (( sqrt ( 1 + x ^(2)) - sqrt (1 - x ^(2)))/( sqrt (1 + ...

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  20. Tan ^(-1) ((a cos x -b sin x)/( b cos x + a sin x ))

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