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d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u ...

`d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u a lto,(0

A

`sec^(2)x`

B

`-sec^(2)((pi)/(4)-x)`

C

`sec^(2)((pi)/(4)+x)`

D

`sec^(2)((pi)/(4)-x)`

Text Solution

AI Generated Solution

To solve the problem of finding the derivative of the function \( y = \sqrt{\frac{1 - \sin 2x}{1 + \sin 2x}} \), we will follow these steps: ### Step 1: Rewrite the Function We start with the function: \[ y = \sqrt{\frac{1 - \sin 2x}{1 + \sin 2x}} \] ...
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CENGAGE ENGLISH-DIFFERENTIATION-Execrises
  1. If y=a sin x + b cos x, then ((dy)/dx)^2+y^2 is

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  2. d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u a lto,(0<x<pi/2), sec^2x (b) ...

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  3. If f(x) = |cos x| + |sin x|, then dy/dx at x = (2pi)/3 is equal to

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  4. If f(x) =|log(e)|x||, then f'(x) equals

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  5. If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a)-(cosx+si...

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  6. Instead of the usual definition of derivative Df(x), if we define a ne...

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  7. " If "y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx...

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  8. if y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/(sqrt(a-x)+sqrt(x-b)) then dy/dx ...

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  9. the derivative of y=(1-x)(2-x)..........(n-x) at x=1 is equal to

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  10. " If "y=sqrt((1-x)/(1+x))," then "(1-x^(2))(dy)/(dx) is equal to

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  11. If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se...

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  12. Let u(x) a n dv(x) be differentiable functions such that (u(x))/(v(x))...

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  13. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/...

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  14. Let h(x) be differentiable for all x and let f(x)=(k x+e^x)h(x) , wher...

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  15. If lim(trarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2...

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  16. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

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  17. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (sqrt(pi)...

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  18. d/dx cos^-1 sqrtcos x is equal to

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  19. if y = tan^-1(2^x/(1+2^(2x+1))) then dy/dx at x =0 is

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  20. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (n y)/(sqrt(x^2+a^2)) (b...

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