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tan ^(-1)""(1-x)/(1+x)- tan ^(-1 )""(1-...

`tan ^(-1)""(1-x)/(1+x)- tan ^(-1 )""(1-y)/(1+y) = sin ^(-1) ""(y-x)/(sqrt((1+x^(2))(1+y^(2)))`

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The correct Answer is:
`(3)/(2)`
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tan ^(-1)""(1-x)/(1+x)""=(1)/(2) sin ^(-1)""(x)/(sqrt(1+x^(2)))

tan ^(-1)x-tan ^(-1)y=sin ^(-1) ""(x-y)/(sqrt((1+x^(2))(1+y^(2)))

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tan^(-1)""(x-y)/(1+xy)+tan^(-1)""(y-z)/(1+yz)+tan^(-1)""(z-x)/(1+zx) =tan^(-1)""(x^(2)-y^(2))/(1+x^(2)y^(2))+tan^(-1)""(y^(2)-z^(2))/(1+y^(2)z^(2))+tan^(-1) ""(z^(2)-x^(2))/(1+z^(2)x^(2))

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If y= tan^(-1) ((sqrt(1+x^(2))-1)/x) , then y'(1) =

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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Short Answer Type Questions)
  1. Find (dy)/(dx) when : tan y=(2t)/(1-t^(2)), sin x=(2t)/(1+t^(2))

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  2. Find (dy)/(dx) when : x=a(2t+sin2t), y=a(1-cos2t)

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  3. tan ^(-1)""(1-x)/(1+x)- tan ^(-1 )""(1-y)/(1+y) = sin ^(-1) ""(y-x)/(...

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  4. Find (dy)/(dx) when : x=cos^(-1)(8t^(4)-8t^(2)+1), y=sin^(-1)(3t-...

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  5. Find (dy)/(dx) when : y=x^(3)* sqrt((x^(2)+4)/(x^(2)+3))

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  6. Find (dy)/(dx) when : y=sqrt(((x-a)(x-b))/((x-c)(x-d)))

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  7. Find (dy)/(dx) when : y=log sqrt((1+sinx)/(1-sinx))

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  8. Find (dy)/(dx) when : y=(x+2)/((x-1)(x+5))

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  9. Differentiate the following functions w.r.t. t : (3^(t) cos t+sin t...

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  10. Differentiate the following functions w.r.t. t : (t^(-2)+t^(2))(2^(...

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  11. Differentiate the following functions w.r.t. t : sqrt(t) e^(t) sec...

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  12. Differentiate the following functions w.r.t. t : (u)/( e^(u) -1)

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  13. Differentiate the following functions w.r.t. t : (u sin u+cos u)/(u...

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  14. If x=a(theta+sin theta) and y=a(1+cos theta), then find the simplified...

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  15. If x=(sin^(3)t)/(sqrt(cos 2t)) and y=(cos^(3)t)/( sqrt(cos 2t)), show...

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  16. Find the differential coefficient of : (tan^(-1)x)/(1+tan^(-1)x)" ...

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  17. Find the differential coefficient of : "tan"^(-1)(sqrt(1+x^(2))-1)/...

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  18. Find the differential coefficient of : "cos"^(-1)(1-x^(2))/(1+x^(2...

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  19. Find the differential coefficient of : x^(sin^(-1)x)" w.r.t. " sin...

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

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