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If x^y = e^(x-y) then prove that (dy)/(d...

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

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SHARAM PUBLICATION-MODEL QUESTION PAPER 13-EXERCISE
  1. Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

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  2. Find the value of k, so that the function defined by f(x)={(kx+1", if...

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

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  4. If x=asec theta, y=b tan theta, then prove that (d^(2)y)/(dx^(2))=-(b^...

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  5. Find the points on the curve x^(2) + y^(2) - 2x - 3 = 0 at which the t...

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  6. For which value of x, the function f(x)=4-x-x^2is maximum or minimum.

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  7. Evaluate int (x+3)^2dx

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  8. Evaluateint0^pi (2/4)sinsqrtxdx

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  9. Evaluate int sin^-1 x dx

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  10. Find the area bounded by the line y = 2x, x- axis and the ordinate x =...

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  11. Solve(dy)/(dt)=e^(3t+5y)

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  12. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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  13. If veca = (2,-2,1), vecb = (2,3,6) and vecc = (-1,0,2), Find the magni...

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  14. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  15. Find the equation of the plane passing through (3,-6,-9) and parallel ...

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  16. If f:RrarrR,g :RrarrR and h : RrarrR such that f(x)=x^2, g(x)= tan x a...

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  17. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  18. Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =...

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  19. Evaluate int0^(pi//2) (cos x)/ ((2+ sin x)(3+sin x))dx

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  20. Find the area of the region between the curves y=cos x" and "y=sinx,x ...

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