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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:
`=2^(x+1).log2//(1+4^(x))`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIATION-Exercise-9(c )
  1. Find the derivatives of the following function. x.logx.log(logx)

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

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

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

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

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

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

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

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

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

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

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

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

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  14. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) then prove that dy/dx=(sqrt(1-y^...

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  15. If y=xsqrt(a^(2)+x^(2))+a^(2)log(x+sqrt(a^(2)+x^(2))), then show that ...

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  16. If x^(logy)=logx then find dy/dx.

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  17. If y = tan^(-1)((3x-x^(3))/(1-3x^(2))) + tan^(-1) ((4x-4x^(3))/(1-6x^(...

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  18. If x^(y)=y^(x) then show that dy/dx=(y(xlogy-y))/(x(ylogx-x)).

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  19. If x ^(3) + y ^(3) =3 axy then (dy)/(dx) =

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  20. Find the derivative dy/dx of the function y=((1-2x)^(2//3)(1+3x)^(-3//...

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