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If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x...

If `y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2])` and `0 < x < 1,` then find `(dy)/(dx)`

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. Solve y=tan^(-1)((sqrt(1+x^2)-1)/x)

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  2. If f(x)=sin^(-1)((2^(x+1))/(1+4^x)) , find f^(prime)(0) .

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  3. If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2]) and 0 < x < 1, then find...

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  4. Find (dy)/(dx) for y=tan^(-1)sqrt((a-x)/(a+x),)-a<x<adot

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  5. The function f(x)=e^x+x , being differentiable and one-to-one, has a ...

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  6. Let g(x) be the inverse of an invertible function f(x) which is diff...

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  7. If f(x) = x + tanx and g(x) is inverse of f(x) then g'(x) is equal to ...

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  8. Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x...

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  9. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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  10. "F i n d"(dy)/(dx)"if"y=tan^(-1)((sqrt(1+x^2)-1)/x), where x!=0

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  11. y=tan^(-1)(3a^2x-x^3)/(a(a^2-3x^2))

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  12. y=sin^(-1)((5x+12sqrt(1-x^2))/(13))

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  13. Find (dy)/(dx) of y=tan^(-1)(x/(1+sqrt(1-x^2)))

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  14. y=tan^(-1)((acosx-bsinx)/(bcosx+asinx)), where -pi/2ltxltpiand a/btanx...

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  15. y= tan^(-1)(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)) then dy...

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  16. Find (dy)/(dx) of y=(sinx)^x+sin^(-1)sqrt(x) .

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

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  18. Find the derivative of y=cos^(-1)((1-x^2)/(1+x^2)) , 0<x<1

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  19. Find the derivative of y=sin^(-1)(2xsqrt(1-x^2))

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  20. If y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2)),="" then="" find="" (dy)/(d...

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