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If y=x^(e^(x)), then the value of (dy)/...

If `y=x^(e^(x))`, then the value of `(dy)/(dx)` is -

A

`y(log x+e^(x))`

B

`y log x(e^(x)+(1)/(2))`

C

`y e^(x)(log x+(1)/(x))`

D

`y e^(x) (x+log x)`

Text Solution

Verified by Experts

The correct Answer is:
C
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 2
  1. If f(x)=cos^(-1)[(1-(logx)^(2))/(1+(logx)^(2))], then the value of f'...

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  2. If y=a cos m x-b sin m x, then the value of (d^(2)y)/(dx^(2)) is -

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  3. If y=x^(e^(x)), then the value of (dy)/(dx) is -

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  4. If 2^(x)+2^(y)=2^(x+y), then the value of (dy)/(dx) at x=y=1 is -

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  5. If f(x)=x(x-1)(x-2), 0 le x le 4, then the point x=c which satisfies m...

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  6. Let f(x)=x|x|. Then the set of points where f(x) is twice differentiab...

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  7. If x=sin^(-1) t, y=log(1-t^(2)), 0 le t lt 1, then the value of (d^(2...

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  8. If 2a+3b+6c=0 " "(a, b, c in R), then the quadratic equation ax^(2)...

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  9. If y=(x+sqrt(1+x^(2)))^(n), then (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(d...

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  10. If sin y+e^(-x cos y)=e, then the value of (dy)/(dx) at (1, pi) is -

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  11. If x=2 cos t+cos 2t and y=2 sin t-sin2t, then the value of (dy)/(dx) a...

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  12. The value of lim(x to oo) (sqrt(x^(2)+ax)-x) is -

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  13. If logx=z, then the value of x^(2)(d^(2)y)/(dx^(2)) is -

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  14. The value of int e^(sqrt(x)) dx is -

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  15. If int x sin x dx = - x cosx +m, then the value of m is -

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  16. The value of int (a^(sqrt(x)))/(sqrt(x))dx is -

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  17. The value of int (e^(tan^(-1)x)dx)/(1+x^(2)) is -

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  18. The value of int(0)^((pi)/(2))(dx)/(1+cotx ) is -

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  19. If I(1)=int(e )^(e^(2)) (dx)/(log x) and I(2)= int(1)^(2)(e^(x))/(x)...

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  20. If I(n)=int(0)^((pi)/(4))tan^(n)thetad theta, for any positive intege...

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