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Differntiate the following functions by ...

Differntiate the following functions by proper substitution.
`[((1+t^2)/(1-t^2))^2-1]^(1/2)`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  1. If y=x+e^(x),then find d^(2)x/dy^(2).

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  2. If e^(x)+e^(y)=e(x+y) find dy/dx.

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  3. Differntiate the following functions by proper substitution. [((1+t^2)...

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  4. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  5. Find dy/dx if log sqrt(x^2+y^2)=tan^(-1) (y/x)

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  6. sinx=2t/1+t^(2), tany=2t/1-t^(2), find dy/dx.

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  7. Find dy/dx, x=3 cos t-2cos^3t, y=3sint-2sin^3t.

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  8. If y=sin(mcos^(-1)x) then prove that (1-x^(2))y(2)-xy(1)+m^(2)y=0.

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  9. If y=cos^(-1)((2cosx-3sinx)/sqrt13), then find dy/dx.

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  10. Examine the continuity of the following functions at indicated points....

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  11. Show that f(x)={(x sin frac{1}{x}, xne0),(o,x=0):} is continuous at x...

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  12. Prove that e^x-2=0 has a solution between 0 and 1.

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  13. So that x^5+x+1=0 for some value of x between -1 and 0.

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  14. Examine continuity and differentiability f(x)={[(1-e^(-x))/x,x!=0],[1,...

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  15. If x=2costheta-cos2theta , y= 2sintheta-sin2theta then find d^(2)y/dx^...

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  16. If y =(sin^(-1) x)^2, prove that (1-x^2)y2 - xy1 - 2 = 0

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  17. Find dy/dx for the following . y=log(2)sqrtsinphi(x).

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  18. Find dy/dx if (x/a)^(2/3) + (y/b)^(2/3) = 1

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  19. Find dy/dx if y = x cot^(-1) (x/y)

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  20. Find dy/dx if (cosx)^(y)=(siny)^(x)

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