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If x^(y) + y^(x) = a^(b) then prove tha...

If `x^(y) + y^(x) = a^(b)` then prove that `(dy)/(dx)=-[(yx^(y-1)+y^(x)Logy)/(x^(y)Logx+xy^(x-1))]` .

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The correct Answer is:
`-((y.x^(y-1)+y^(x).logy))/((x^(y).logx+x.y^(x-1)))`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIATION-Exercise-9(c )
  1. If y=xsqrt(a^(2)+x^(2))+a^(2)log(x+sqrt(a^(2)+x^(2))), then show that ...

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  2. If x^(logy)=logx then find dy/dx.

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  3. If y = tan^(-1)((3x-x^(3))/(1-3x^(2))) + tan^(-1) ((4x-4x^(3))/(1-6x^(...

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  4. If x^(y)=y^(x) then show that dy/dx=(y(xlogy-y))/(x(ylogx-x)).

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  5. If x ^(3) + y ^(3) =3 axy then (dy)/(dx) =

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  6. Find the derivative dy/dx of the function y=((1-2x)^(2//3)(1+3x)^(-3//...

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  7. Find the derivative (dy)/(dx) of each of the following functions. y=...

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  8. Find (dy)/(dx) for the function (using logarithms). y = ((a - x ) ^(...

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  9. Find (dy)/(dx) for the function (using logarithms). y = (x ^(3) sqrt...

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  10. Differentiate sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5))).

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  11. Find the derivative of (sinx)^(log x)+x^(sinx).

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  12. Find the derivatives of the following functions. x^(x^(x))

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  13. Find the derivative of (ii) (sinx)^(x)+x^(sinx) w.r.to x.

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  14. Find the derivatives of the following functions. x^(3)+(cotx)^(x)

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  15. If x^(y) + y^(x) = a^(b) then prove that (dy)/(dx)=-[(yx^(y-1)+y^(x)L...

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  16. If f(x) = sin^(-1) sqrt((x-beta)/(alpha-beta)), g(x) = tan^(-1) sqrt((...

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  17. If f(x)=(a^(2)-b^(2))^(-1//2).cos^(-1)((acosx+b)/(a+bcosx)) a gt b gt ...

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  18. Differentiate (x^(2)-5x+8)(x^(3)+7x+9) by Using product rule

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  19. Differentiate (x^(2)-5x+8)(x^(3)+7x+9) by Using product rule

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  20. Differentiate (x^(2)-5x+8)(x^(3)+7x+9) by Using product rule

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