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If y=sqrt((1-x)/(1+x)), prove that (1-x^...

If `y=sqrt((1-x)/(1+x)),` prove that `(1-x^2)dy/(dx)+y=0`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Differentiate y=(e^x)/(1+sinx)

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  2. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

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  3. If y=sqrt((1-x)/(1+x)), prove that (1-x^2)dy/(dx)+y=0

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  4. If g(x)=(f(x))/((x-a)(x-b)(x-c)),where f(x) is a polynomial of degree ...

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  5. If f(x)=cosxdotcos2xdotcos4xdotcos8xdotcos16 x , then find f^(prime)(p...

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  6. f(x)=e^(-1/x),w h e r ex >0, Let for each positive integer n ,Pn be th...

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  7. If ai, bi in N for i 1,2,3, then coefficient of x in the determinant;|...

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  8. If d/(dx)[(x^m-A1x^(m-1)+A2x^(m-2)-.......+(-1)^m Am)e^x]=x^m e^x , f...

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  9. If y= |[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1,1]|, find (dy)/(dx)

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  10. Let f(x)a n dg(x) be two function having finite nonzero third-order de...

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  11. Differentiate log sinx w.r.t. sqrt(cosx).

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

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

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

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

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

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

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

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

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

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