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Differentiate the functions given w.r.t....

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

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The correct Answer is:
`(x+1/x)^(x)[(x^(2)-1)/(x^(2)+1)+log(x+1/x)]+x^(1+1/x)[(x+1-logx)/x^(2)]`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(i) (LONG ANSWER TYPE QUESTIONS (I))
  1. y=e^(sinx)+(tanx)^(x)

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  2. Differentiate the following w.r.t. x : x^(x)-2^(sinx)

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

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

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  5. Differentiate the following w.r.t. x : x^(x)+(sinx)^(x)

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  6. Differentiate the following w.r.t. x : ((ax+b)(cx+d))/((ax-b)(cx-d))...

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

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  8. Differentiate the following w.r.t. x : x^(2)e^(x)sinx

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  9. Differentiate the following w.r.t. x : e^(x)cos^(3)xsin^(2)x

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  10. Differentiate the following w.r.t. x : (x+3)^(2)(x+4)^(3)(x+5)^(4)

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  11. Differentiate the following w.r.t. x : sqrt((x-1)(x-2)(x-3)(x-4))

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  12. If x y=e^(x-y) , find (dy)/(dx) .

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  13. If (sinx)^(y)=(siny)^(x),"find "dy/dx.

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  14. Find dy/dx" if "(sinx)^(cosy)=(cosy)^(sinx).

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  15. Differentiate log(x^(x)+cosec^(2)x) w.r.t. x.

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  16. If x^(p)y^(q)=(x+y)^(p+q), show that dy/dx=y/x.

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  17. If y=x^(y), show that dy/dx=y^(2)/(x(1-ylogx))

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  18. If y^(x)=e^(y-x), then prove that (dy)/(dx) = ((1+logy)^(2))/(logy)

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  19. If x^x+y^x=1 , prove that (dy)/(dx)=-{(x^x(1+logx)+y^x logy)/(x y^((x...

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  20. If x^(y)+y^(x)=1,"find "dy/dx

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