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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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MAXIMUM PUBLICATION-CONTINUITY & DIFFERENTIABILITY-EXAMPLE
  1. Find dy/dx if x^3+2x^2y+3xy^2+4y^3=5

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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 of y=sin^-1(3x-4x^3)+cos^-1(4x^3-3x)

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  5. Find dy/dx of y=tan^-1(sqrt((1-cosx)/(1+cosx)))

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  6. Consider the function f(x)=absx , x in R Draw the graph of f(x)= abs...

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  7. Consider the function f(x)=absx , x in R Show that the function is c...

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  8. Find the derivative of y=x^a+a^x with respect to x.

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  9. If e^y(x+1)=1 , show that (d^2y)/(dx^2)=(dy/dx)^2

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

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

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

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

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  14. Consider a function f:RrarrR defined by f(x)={(a+x,xle2),(b-x,x>2):}...

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  15. Consider a function f:RrarrR defined by f(x)={(a+x,xle2),(b-x,x>2):}...

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

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

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

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  19. Verify mean value theorem for the function f(x)=x^2-4x-3 in the interv...

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  20. Find 'a' and 'b' if the function f(x)={(sinx/x,-2lexle0),(axx2^x,0le...

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