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prove that d/dx(x^x)=x^x(1+logex)...

prove that `d/dx(x^x)=x^x(1+log_ex)`

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Let the function ln f(x) is defined where f(x) exists for 2 geq x and k is fixed positive real numbers prove that if -k f(x) geq d/(dx) (x.f(x)) then f(x) geq Ax^(-k-1) where A is independent of x.

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PATHFINDER-DERIVATIVES-QUESTION BANK
  1. show that the function f(x)=abs(x-2)+abs(x-3) is not differentiable at...

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  2. If log(x^2-y^2)/(x^2+Y^2)=a the prove that (dy/dx)=y/x

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  3. prove that d/dx(x^x)=x^x(1+logex)

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  4. y=x^(x^(x^------infty) then prove that dy/dx=(y^2)/(x(1-ylogx))

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  5. If y=tan^(-1)(5ax)/(a^2-6x^2) prove that dy/dx=(3a)/(a^2+9x^2)+(2a)/(a...

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  6. y=sin^(-1)(xsqrt(1-x)+sqrtxsqrt(1-x^2)) show that dy/dx=(1)/(sqrt(1-x^...

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  7. f(x) is differentiable at x=a prove that underset(xrarra)Lt ((x+a)f(a)...

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  8. If y=g{g(x)}, g(0)=0 and g'(0)=2 then find dy/dx at x=0

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  9. 2f(x)+3f(-x)=x^2-x+1 then determine f'(1)

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  10. x=sectheta-costheta , y=sec^n theta- cos^n theta show that (dy/dx)^2=(...

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  11. y=tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) show that dy/d...

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  12. f(x)=5x-4 (0ltxle1) =4x^2-3x (1ltxlt2) test whether f(x) is differenti...

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  13. find the derivative of x^x

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  14. Find by the defination the differential coefficient of the following: ...

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  15. Find derivative of the following: sec3x

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  16. Find derivative of the following:e^(sqrtx)

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  17. Find derivative of the following: sin^(-1)x

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  18. Find by the definition the differential coefficient of the following: ...

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  19. Find by the definition the differential coefficient of the following:l...

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  20. Find by the definition the differential coefficient of the following: ...

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