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

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

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Choose the correct answer from the bracket. If x=sin t and y= cos t, t...

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  2. Find the value of k such that the function f(x) defined by f(x)={(kx-1...

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

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  4. Find the value of a such that the function f(x) defined by f(x)={(ax+3...

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  5. If x=acos^3theta and y=asin^3theta. Prove that 1+(dy/dx)^2=sec^2theta.

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  6. Choose the correct answer from the bracket. If x=at^2,y=2at, then the ...

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  7. Is the function defined by f(x)={(x+3,ifxle1),(x-3,ifx>1):} a continuo...

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  8. Find dy/dx, if y=tan^-1((cosx-sinx)/(cosx+sinx))

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  9. If x^(2)+2xy+2y^(2)=1, then (dy)/(dx) at the point where y=1 is equal ...

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  10. Find the relationship between a and b so that the function f defined b...

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  11. If x^yy^x=16, then find dy/dx at (2,2).

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  12. Verify Lagranges' Mean value theorem for the function f(x)=2x^2-10x+29...

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  13. If f(x)=log[e^(x)((3-x)/(3+x))^(1//3)] then f'(1) is equal to a)(3)/(4...

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  14. Verify Rolle's theorem for the function f(x)=sin3x on [0,pi/3].

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  15. Let y=(x+sqrt(1+x^2))^m Find dy/dx.

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  16. Let y=(x+sqrt(1+x^2))^m Show that (1+x^2)(d^2y)/dx^2+xdy/dx-m^2y=0.

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  17. Find dy/dx if sinx+cosy=xy

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  18. Find dy/dx if y=(sinx)^(logx).

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  19. Differentiate the following. sin[sqrt(sinsqrtx)].

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  20. Differentiate the following :y=tan^-1[(sqrt(1+x^2)+1)/x]

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