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If x=e^(x//y), prove that (dy)/(dx) = (x...

If `x=e^(x//y), `prove that `(dy)/(dx) = (x-y)/(xlogx)`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following functions w.r.t.x : x^(tanx) + sqrt((x^2...

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  2. Differentiate the following functions w.r.t.x : (cosx)^x + (sinx)^(1...

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  3. If x=e^(x//y), prove that (dy)/(dx) = (x-y)/(xlogx)

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

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  5. If x^p.y^q=(x+y)^(p+q) , show that dy/dx=y/x ;

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  6. If y = x^(x^(x….. To infty), prove that dy/dx = y^2/(x(1-ylogx)).

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  7. Differentiate (sinx)^(x)+(cosx)^(sinx) w.r.t. x.

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  8. Differentiate the following functions w.r.t.x x^x + x^(1//x)

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  9. Differentiate the following functions w.r.t.x x^(sinx) + (sin x)^x

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  10. Differentiate the following functions w.r.t.x (sinx)^(cosx) - x^(1//x)

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  11. Differentiate the following functions w.r.t.x sin(x^x) + (sin x)^x

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  12. Differentiate the following functions w.r.t.x x^(tanx) + (tanx)^(sinx)

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  13. Differentiate the following functions w.r.t.x : x^(sinx) + sinx^(cos...

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  14. Differentiate the following functions w.r.t.x (x cos x )^x + (x sin x ...

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  15. Differentiate (x^x)^x w.r.t.x .

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  16. Find dy/dx when y = 10x^x + x^(x^x) + (x^10)

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  17. Find dy/dx when y = e^(e^(e^x)) + e^(x^(e^(x))) + e^(e^(x^x))

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  18. Find dy/dx when (sin x)^y = (sin y)^x

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  19. Find (d^2y)/(dx^2) when y = 2x^3 + 3x^2 + 6

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  20. Find (d^2y)/(dx^2) when y = (logx)/(x)

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