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If x^x + y^x = 1, prove that : dy/dx = -...

If `x^x + y^x = 1`, prove that : `dy/dx = -[(x^x (1+logx) + y^x.logy)/(x.y^((x-1)))]`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If y = x^y, prove that (dy)/(dx) = (y^2)/(x(1 - y log x))

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  2. Differentiate the following w.r.t.x. If y^x = e^(y - x), prove that ...

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  3. If x^x + y^x = 1, prove that : dy/dx = -[(x^x (1+logx) + y^x.logy)/(x....

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  4. If x^y + y^x=1, find dy/dx

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  5. If x^y + y^x = log a, find dy/dx.

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  6. Show that if x^y + y^x = m^n, then: dy/dx = - (y^x logy +yx^(y-1))/...

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  7. Find the derivative of the function given by f(x) = (1+x)(1+x^2)(1+x^4...

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

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  9. Differentiate(x^2-5x+8)(x^3+7x+9) by expanding the product to obtain a...

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  10. Differentiate (x^2-5x+8)(x^3+7x+9) by logarithmic differentiation.

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  11. If y = (sqrtx)^(sqrtx^(sqrtx))......... to infty), prove that dy/dx = ...

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  12. If y = sqrt(x+ sqrt(x + sqrt(x + ......oo))), show that (2y - 1) (dy)/...

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  13. If y = sqrt(3^x+sqrt(3^x+sqrt(3^x+….......oo))), then prove that : (2y...

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  14. If y = x^y, prove that (dy)/(dx) = (y^2)/(x(1 - y log x))

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  15. If y = (cosx)^(cosx^(cosx……..to infty)) prove that dy/dx = (-y^2 tanx)...

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  16. If y=(tanx)^((tanx)^((tanx)^...oo)), then prove that (dy)/(dx)=2 at x=...

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  17. If y = (x^(x^(x)….......to oo)), prove that xdy/dx=y^2/(1-ylogx).

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  18. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : 1+2x

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  19. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : ax^3...

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  20. Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : 1/(2...

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