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"F i n d"(dy)/(dx)"if"y=tan^(-1)((sqrt(1...

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

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x...

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

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

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

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

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

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

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

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

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

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

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

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  14. Find the derivative of cos^(-1)(sinx) w.r.t. to x

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  15. Find the derivative of tan^(-1)((sinx)/(1+cosx)) w.r.t. to x

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

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  17. Find (dy)/(dx) if x=a(theta-sintheta) and y=a(1-costheta) .

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  18. If x=asec^3theta and y=atan^3theta , find (dy)/(dx) at theta=pi/3

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  19. Find (dy)/(dx) if x=a(cost+tsint) and y=a(sint-tcost)

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  20. Find (dy)/(dx) if x=(3a t)/(1+t^3) ; y=(3a t^2)/(1+t^3)

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