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Find (dy)/(dx) when : y=sqrt(((x-a)(x...

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

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Verified by Experts

The correct Answer is:
`(1)/(2) sqrt(((x-a)(x-b))/((x-c)(x-d)))[(1)/(x-a)+(1)/(x-b)-(1)/(x-c)-(1)/(x-d)]`
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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Short Answer Type Questions)
  1. Find (dy)/(dx) when : x=cos^(-1)(8t^(4)-8t^(2)+1), y=sin^(-1)(3t-...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If y=e^((y)/(x)) show that, (dy)/(dx)=(y^(2))/(x(y-x)).

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  19. If ye^(y)=x, prove that, (dy)/(dx)=(y)/(x(1+y)).

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  20. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), show that, (dy)/(dx)=(sqrt(1-...

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