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Differentiate the following w.r.t. x : ...

Differentiate the following w.r.t. x :
`(x + 1/x)^x + x^(x + 1/x)`

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The correct Answer is:
`(x + 1/x)^x [(x^2 - 1)/(x + 1) + "log" (x + 1/x)] + x^(1 + 1/x)((x + 1 - log x)/(x^2))`
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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. Find the values of k so that the function f is continuous at the indic...

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  2. If (cos x)^y = (cos y)^x, find dy/dx .

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  3. Differentiate the following w.r.t. x : (x + 1/x)^x + x^(x + 1/x)

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  4. Differentiate the following w.r.t. x : x^(x^2 - 3) + (x - 3)^(x^2) ,...

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  5. For what value of k, function f (x) is continuous at x = 0 where f(x) ...

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  6. Find (dy)/(dx) when x^y + y^x = a^b

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  7. Differentiate tan^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + ...

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  8. y = e^(m sin^(-1)x), prove that (1 - x^2) y2 - xy1 = m^2y

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  9. If y = e^(m tan^-1 x), then show that (1 +x^2) y2 + (2x - m) y1= 0.

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  10. Examine the continuity of f(x) = {{:((x)/(|x| )"," ,"if " x != 0),(0",...

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  11. If xy = e^(x - y), prove that (dy)/(dx) = (y (x - 1))/(x (y + 1))

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  12. Differentiate e^(sec^2 x) + 3 cos^(-1) x w.r.t.x.

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  13. Find k so that f(x) = {{:((x^2 -25 )/(x -5)"," ,"if " x != 5),(k",","...

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  14. If f(x) is continuous at x = 0 , find a, where f(x) = {{:((1 - cos ax)...

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  15. Differentiate tan^(-1) ((sqrt(1 + x^2) - 1)/(x)) w.r.t.x .

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  16. Differentiate tan^(-1)((sqrt(1 + a^2 x^2) - 1)/(ax)) w.r.t.x.

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  17. Verify LMV theorem for the following functions f(x) = x(x-1)(x - 2) i...

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  18. Verify LMV theorem for the following functions f(x) = x^2 + x - 1 "...

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  19. Discuss the continuly of the following functions f(x) = {{:(2x"," , ...

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  20. Discuss the continuly of the following functions f(x) = {{:(2"," , "...

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