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Write the following function in the simp...

Write the following function in the simplest form :
`"tan"^(-1)(sqrt(1+x^(2))-1)/x, x!=0`

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The correct Answer is:
`(l)/(2(l+x^(2)))`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIATION-Exercise-9(c )
  1. Find the derivative of Tan^(-1)((3a^(2)x-x^(3))/(a(a^(2)-3x^(2)))).

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  2. Simplify each of the following: tan^(-1)(Secx+tanx)

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  3. Write the following function in the simplest form : "tan"^(-1)(sqrt(...

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  4. Find the derivatives of the following function. (logx)^(tanx)

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  5. Find the derivatives of the following function. (x^(x))^(x)=x^(x^(2)...

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  6. Find the derivative of 20^(log(tanx)).

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  7. Find the derivative of the w.r.to x. x ^(x) + e ^(e ^(x))

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  8. Find the derivatives of the following function. x.logx.log(logx)

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  9. Find the derivative of e ^(- ax ^(2)) .sin (x log x ) w.r.t.x

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

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  11. Find (dy)/(dx) for the following functions. x=3cos t-2 cos^(3)t, ...

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  12. If x=(3at)/(1+t^(3)),y=(3at^(2))/(1+t^(3)) then find dy/dx.

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  13. Find (dy)/(dx) if x =a ( cos t + t sin t ), y = a ( sin t - t cos t...

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  14. If x=a[(1-t^(2))/(1+t^(2))],y=(2bt)/(1+t^(2) then find dy/dx.

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  15. Differentiate f(x)=log(a)x with respect to g(x)=a^(x).

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  16. Differentiate f(x) with respect to g(x) for the following . f(x)=sec...

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

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  18. Find the derivative of x^(4)+y^(4)-a^(2)xy=0.

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  19. Find the derivative of y=x^(y).

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  20. Find the derivative of the function y defined implicitly by each of th...

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