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sin ^(-1) ((2^(x +1))/( 1 + 4 ^(x))) ({:...

`sin ^(-1) ((2^(x +1))/( 1 + 4 ^(x))) ({:(put), ( 2 ^(x) = tan theta ):})`

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The correct Answer is:
x`(2 ^(x +1) log 2)/( 1 + 4 ^(x))`
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AAKASH SERIES-DIFFERENTIATION -EXERCISE -4.6
  1. Find the derivative of the function wrt x. Sec ^(-1) ((1)/( sqrt (1 ...

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

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  3. Find the derivative of Sec^-1(1/(2x^2-1))

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  4. Find the derivative of Sin^(-1)((2x)/(1+x^(2))).

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  5. Tan ^(-1) ((2x)/( 1 - x ^(2)))

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  6. sin ^(-1) ((2^(x +1))/( 1 + 4 ^(x))) ({:(put), ( 2 ^(x) = tan theta ):...

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  7. The derivative of Cos ^(-1) (4x ^(3) -3x) w.r.t x is

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  8. Find the second order derivative of Tan^(-1)((3x-x^(3))/(1-3x^(2))).

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  9. Find the derivative of f (x) w.r.t. g(x) for the f (x) = e ^(x), g (...

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  10. Find the derivative of f (x) w.r.t. g(x) for the f(x) = e ^(sinx), g...

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  11. Find the derivative of f (x ) = Tan ^(-1) ((2x )/( 1 - x ^(2))) w.r.t ...

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  12. Find the derivative of f (x) w.r.t. g(x) for the f (x) = Tan ^(-1) (...

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  13. Find the derivative of f (x) w.r.t. g(x) for the f (x) = Sec ^(-1) (...

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  14. Find the derivative of f (x) w.r.t. g(x) for the f (x) = log x, g (x...

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  15. Find (dy)/(dx) in the following : y = tan^(-1)((3x-x^(3))/(1-3x^(2))...

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  16. Find (dy)/(dx) in the following : y= cos^(-1) ((1-x^(2))/(1+x^(2))),...

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  17. If y = Sin ^(-1) (1 - x ^(2))/(1+ x ^(2)) then (dy)/(dX)=

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  18. Find (dy)/(dx) in the following : y= cos^(-1) ((2x)/(1+x^(2))), -1 l...

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  19. Find (dy)/(dx) in the following : y= sin^(-1) (2x sqrt(1-x^(2))), (1...

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  20. If y=sec^(-1)((1)/(2x^2-1)) find (dy)/(dx).

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