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If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/...

If `y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s` (a)`(-2)/(1+x^2)` for all `x` (b) `(-2)/(1+x^2)` for all `|x|<1` (c)`2/(1+x^2)` for `|x|>1` (d) none of these

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If x in (0,pi/2), then show that cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48...

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  2. "If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," th...

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

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

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

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

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

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  11. If y=sqrt(sinx+y), then find (dy)/(dx)

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  12. f(x)=|x^2-3|x|+2|dot Then which of the following is/are true f^(prime)...

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  13. If xsqrt(1+y)+ysqrt(1+x)=0, prove that dy/dx=(-1)/((1+x)^2

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  14. If x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then (a)y^(prime)(1)=4/3 (b) y...

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  15. If x^y=e^(x-y), Prove that dy/dx=logx/(1+logx)^2

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  16. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot Then (a)f^(prime)(10...

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  17. If sqrt(x) +sqrt(y)=4, f i n d (dx/dy) a t (y = 1).

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  18. If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1) and (dy)/(dx)=a x+b , then the value...

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  19. If x y+y^2=tanx+y ,then find (dy)/(dx)

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  20. Find (dy)/(dx) for y=sin^(-1)(cosx)

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