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If f(x)=logx(logex) then f'(e)=...

If `f(x)=log_x(log_ex)` then `f'(e)`=________

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A DAS GUPTA-Differentiation-Exercise
  1. Find the sum of series sum(r=1)^nr.x^(r-1), using calculus.

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  2. Differential coefficient of log2(log2x)w.r.t x is

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  3. If f(x)=logx(logex) then f'(e)=

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  4. If x=a (cos t +log (tan ((t)/(2)) )) ,y =a sin t ,then (dy)/(dx) =

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  5. Let f'(x) = sin(x^2) and y = f(x^2 +1) then dy/dx at x=1 is

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  6. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

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  7. If f'(x)=sin x^2 and y=f(x^2+1) then dy/dx=

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  8. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

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  9. If tany = (2t)/(1-t^2) and sin x = (2t)/(1+t^2) then (dy)/(dx)=

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  10. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

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  11. If x^2y +y^3=2, the value of (dy)/(dx) at the point (1,1) is

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  12. Let f(x)={(tan)pi/4+tanx}{(tan)pi/4+(tan)(pi/4-x)}and g(x)=x^2+1. Then...

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  13. IF y = 1 / (1+ x + x^2 + x^3), then value of (d^2y) / dx^2 at x = 0 is

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  14. IF y = 1 / (1+ x + x^2 + x^3), then value of (d^2y) / dx^2 at x = 0 is

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  15. If y=log (x+5), x!= -5 then dy/dx=

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  16. If x^y = e^(x-y) " then " dy/dx ?

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  17. If x=e^tcos t,y=e^t sin t then (dy)/(dx)=

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  18. If phi(x)= |[1,2x,3x^2], [x,x^2,x^4], [0,2,6x]| then phi'(1)=

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  19. The value of (dy/dx){(1,1)} for the curve 2y = 3 -x^2 is

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  20. Let y =log(e)sin(x^2),0ltxlepi/2. The value of dy/dx at x= sqrt(pi/2) ...

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