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Find (dy)/(dx) of the functions x^(y) + ...

Find `(dy)/(dx)` of the functions `x^(y) + y^(x)=1`

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The correct Answer is:
`(-(y^(x) log y + x^(y-1) .y))/(x^(y).log x+ y^(x-1)x)`
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Exercise-5.5
  1. Differentiate the functions x^(x cos x) + (x^(2) + 1)/(x^(2)-1)

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  2. Differentiate the functions (x cos x)^(x) + (x sin x)^((1)/(x))

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  3. Find (dy)/(dx) of the functions x^(y) + y^(x)=1

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  4. Find (dy)/(dx) of the functions y^(x)= x^(y)

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  5. Find (dy)/(dx) of the functions (cos x)^(y)= (cos y)^(x)

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  6. Find (dy)/(dx) of the functions given in Exercises 12 to 15. xy= e^(...

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  7. Find the derivative of the function given by f(x) = (1 + x) (1 + x^(2)...

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  8. Differentiate (x^(2)-5x + 8) (x^(3) + 7x + 9) By using product ru...

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  9. Differentiate (x^(2)-5x + 8) (x^(3) + 7x + 9) in three ways mentioned ...

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  10. Differentiate (x^(2)-5x + 8) (x^(3) + 7x + 9) in three ways mentioned ...

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  11. If u, v and w are functions of x, then show that (d)/(dx) (u.v.w) = (d...

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  12. If u, v and w are functions of x, then show that (d)/(dx) (u.v.w) = (d...

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  13. Differentiate the functions cos x.cos 2x. Cos 3x

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  14. Differentiate the functions sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))

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  15. Differentiate the functions (log x)^(cos x)

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  16. Differentiate the functions x^(x)-2^(sin x)

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  17. Differentiate the functions (x+ 3)^(2).(x+ 4)^(3).(x+ 5)^(4)

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  18. Differentiate the functions (x + (1)/(x))^(x) + x^((1 + (1)/(x)))

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  19. Differentiate the functions (log x)^(x) + x^(log x)

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  20. Differentiate the functions (sin x)^(x) + sin^(-1) sqrtx

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