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IF x^y=e^(x-y) then show that (dy)/(dx)=...

IF `x^y=e^(x-y)` then show that `(dy)/(dx)=(logx)/[log(xe)]^2`.

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. Find (dy)/(dt), when y=sin^(-1)(2sqrt(t^(2)-1)/(t^(2)))

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

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  3. IF x^y=e^(x-y) then show that (dy)/(dx)=(logx)/[log(xe)]^2.

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  4. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  5. If x=a(cost+tsint) and y=a(sint-tcost), then find (d^(2)y)/(dx^(2)) at...

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  6. If cosx=sqrt(1/(1+t^2)),sin y=(2t)/(1+t^2) then show that (dy)/(dx) is...

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  7. Find (dy)/(dx), when y^(x)=x^(siny)

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  8. If y^2 cot x = x^2 cot y then find (dy)/(dx).

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  9. Find the derivative of x^(sinx) w.r.t.x.

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  10. Differentiate sin^(-1) ((2X)/(1+X^(2))) with respect to cos^(-1) ((1-X...

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  11. Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...

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  12. Differentiate y=(siny)^(sin2x)

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  13. Test the differentiability and continuity of the following function at...

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  14. What is the derivative of sec^(-1)(1/(2x^2-1)),with respect to(sqrt(1...

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  15. If y=(x+(1)/(x+(1)/(x+ . . .oo))) find (dy)/(dx), the rhs being a vali...

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  16. If y=e^(sin^(-1)x) and u=logx then what is (dy)/(du)?

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  17. Find the slope of the tangent to the curve x=2(theta-sin2theta),y=2(...

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  18. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  19. Differentiate sec^(-1)((x+x^(-1))/(x-x^(-1))) w.r.tx.

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  20. Prove that y=tan(x+y), then (dy)/(dx)=(1+y^(2))/(-y^(2))

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