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"Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha)...

`"Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)) and "tan"(x)/(2)=sqrt((1-alpha)/(1+alpha)),alpha in [-1, 0]cup(0,1]." Then "((dy)/(dx))_(x=(pi)/(3))=`

A

`1//2`

B

1

C

2

D

`1//3`

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The correct Answer is:
C
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CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

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  2. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

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  3. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

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  4. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

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  5. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

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  6. If y=(x^x) then (dy)/(dx) is

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  7. The first derivative of the function [cos^(-1)(s insqrt((1+x)/2))+x^x]...

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  8. f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)'...

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  9. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

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  10. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

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  11. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f prime prime(x...

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  12. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto 2^(20)(cos2x-2^(20)os3x...

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  13. (d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d...

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  14. The nth derivative of the function f(x)=1/(1-x^2) [where x in(-1,1) a...

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  15. If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a)(x(dy)/(dx)-y)^2 (b)...

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  16. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

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  17. If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y2+x y1 is (where yr represen...

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  18. If (sinx)(cosy)=1/2,t h e n(d^2y)/(dx^2)a t(pi/4,pi/4) is -4 (b) -2 (c...

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  19. A function f satisfies the condition f(x)=f^(prime)(x)+f^(x)+f^(x) ,w ...

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  20. Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,...

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