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Find (dy)/(dx) of y=x^((log)e x)...

Find `(dy)/(dx)` of `y=x^((log)_e x)`

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

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  2. Find (dy)/(dx) of y=(1+1/x)^x

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  3. Find (dy)/(dx) of y=x^((log)e x)

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  4. Find (dy)/(dx) of y=x^(x^(x))

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  5. Find (dy)/(dx) of y=(sqrt(x)(2x+3)^2)/(sqrt(x+1))

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  6. Find (dy)/(dx) of y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)...

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  7. Find (dy)/(dx) of y=sin2xcos2xcos4x+(log)2 2^(x+3)

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  8. The value of (dy)/(dx) at x=pi/2 , where y is given by y=x^(sinx)+s...

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  9. If ysqrt(x^2+1)=log{sqrt(x^2+1)-x} , then (x^2+1)(dy)/(dx)+x y+1 is eq...

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  10. If y=((log)(cosx)sinx)((log)(sinx)cosx)+sin^(-1)(2x)/(1+x^2) , then (d...

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  11. For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is 1//2 (...

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  12. If siny+e^(-xcosy)=e , then (dy)/(dx) at (1,\ pi) is equal to.........

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  13. If y^x+x^y=a^b , then (dy)/(dx) is equal to........

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  14. If f(x)=e^xg(x), g(0)=2, g'(0)=1 , then f'(0) is equal to.......

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  15. If y=(tanx)^(cotx) , then (dy)/(dx) is equal to......

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  16. If x^p y^q = (x+y)^(p+q) find dy/dx

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  17. If y=(sinx)^(sinx)^(((sinx)dotoo)) , then (dy)/(dx) is equal to..........

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  18. If x=e^(y+e^(y)+..... oo) , x >0 , then (dy)/(dx) is equal to........

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  19. If x^y=y^x , then (dy)/(dx) is equal to......

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  20. If y=sqrt(x+sqrt(x+sqrt(x+ tooo))) , then (dy)/(dx) is equal to.....

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