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Differentiate tan^(-1)((sqrt(1+x^2)-1)/x...

Differentiate `tan^(-1)((sqrt(1+x^2)-1)/x)w.r.t tan^(-1)x ,w h e r ex!=0.`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Differentiate log sinx w.r.t. sqrt(cosx).

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  2. If cosx/2dotcosx/(2^2)dotcosx/(2^3)oo=(sinx)/x , then find the value o...

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  3. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x)w.r.t tan^(-1)x ,w h e r ex!=...

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  4. Find the derivative of f(tan x) w.r.t. g (sec x) at x=(pi)/(4), where ...

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  5. If f(x)=cos^(-1)(1/sqrt(13))(2cosx-3sinx) +sin^(-1)(1/sqrt(13))(2co...

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  6. Find the derivative of tan^(-1)(2x)/(1-x^2) w.r.t sin^(-1)(2x)/(1+x^2)

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  7. If |a1sinx+a2sin2x++ansinn x|lt=|sinx| for x in R , then prove that |...

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  8. Find the derivative of sec^(-1)(1/(2x^2-1)) w.r.t sqrt(1-x^2) at x=1/...

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  9. If y=(1/2)^(n-1)cos(ncos^(-1)x), then prove that y satisfies the diffe...

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  10. If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then ...

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  11. If x in (0,pi/2),t h e ns howt h a t d/(dx)cos^(-1){7/2(1+cos2x)+...

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  12. If f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2|,t h e n prove that ...

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  13. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (a)(-2)/(1+x^2) fo...

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  14. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

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  15. If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0...

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  16. If x^3+y^3+3a x y=0 , f i n d dy / dx

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  17. If 1 is the twice repeated root of the equation a x^3+b x^2+b x+d=0,t ...

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  18. If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y)

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  19. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

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  20. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a)1/(2y-1)...

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