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

If `e^(x-y)=x^y` then prove that `dy/dx=logx/[logex]^2`

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find dy/dx if (sinx)^(cosy) = (cosy)^(sinx)

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  2. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

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  3. If e^(x-y)=x^y then prove that dy/dx=logx/[logex]^2

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  4. Find dy/dx if x^3+2x^2y+3xy^2+4y^3=5

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  5. Find dy/dx if x=2cos^3theta,y=2sin^3theta.

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  6. Find dy/dx of y=sin^-1 2xsqrt(1-x^2) (-1)/sqrt2<x<1/sqrt2

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  7. Find the value of k if the function f(x) = kx+1 if x<5 ...

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  8. Find dy/dx, If x=a(t-sint) , y=a(1+cost)

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  9. Verify Rolle's theorem for the function f(x)=x^2+2 in the interval [...

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  10. Consider f(x)={(3x-8,xle5),(2k,x>5):} . Find the value of k if f(x) is...

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  11. Find dy/dx , if y=(sinx)^logx , sinx>0

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  12. If y=(sin^-1x)^2 , then show that (1-x^2)(d^2y)/(dx^2)-xdy/dx=2

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  13. Determine the value of k so that the function f(x)={(k(x^2+x+1),x<0)...

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  14. If y=[x+sqrt(x^2+9)]^n , show that dy/dx=(ny)/(sqrt(x^2+9)

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  15. Find dy/dx of x=sqrt(a^(sin^-1t) y=sqrt(a^(cos^-1t)

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  16. Find the values of k so that function f is continuous at the indicated...

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  17. Find dy/dx if y=x^sinx,x>0.

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  18. If y=sin^-1x,then show that (1-x^2)(d^2y)/dx^2-xdy/dx=0

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  19. Check the continuity of the function given by f(x)={(xsinfrac1x,xne0),...

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  20. Verify mean value theorem for the function f(x)=x+frac1x in the interv...

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