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f(x) = x^(x)+ x^(1/x), find f'(x)....

`f(x) = x^(x)+ x^(1/x), find f'(x).`

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The correct Answer is:
`x^(x){1+logx}+ x^(1/x){(1-logx)/x^(2)}`
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PREMIERS PUBLISHERS-DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION -PROBLEMS FOR PRACTICE
  1. If y = x^(a)+a^(x)+x^(x)+a^(a), dind dy/dx.

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  2. find dy/dx if y = (logx)^(sin^(-1)x

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  3. f(x) = x^(x)+ x^(1/x), find f'(x).

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  4. y = tan^(-1)((3x-x^(3))/(1-3x^(2))), find dy/dx.

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  5. y = sec^(-1)((1+x^(2))/(1-x^(2))), find dy/dx.

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  6. Find the derivatives of the following : tan^(-1)((cosx+sinx)/(cosx-s...

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  7. If y = tan^(-1)((1+x^(2))/(1-x^(2))) Find dy/dx.

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  8. y = tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(ax))), find dy/dx.

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  9. y = tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))),find dy/dx.

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  10. y = cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))),...

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  11. Differentiate cosec^(-1)(1/(3x-4x^(3))):

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  12. If x=asec^(3)theta " and " y=atan^(3)theta " find " (dy)/(dx) " at " t...

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  13. If x = 2costheta- cos 2theta, y = 2sintheta -sin 2theta, find dy/dx.

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  14. x = a(costheta + logtan(theta/2), y = asintheta, find dy/dx.

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  15. If x^(m)y^(n) = (x+y)^(m+n),find dy/dx.

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  16. If e^(x)+ e^(y) = e^(x+y), find dy/dx.

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  17. If ax^(2) +2hxy + by^(2) + 2gx + 2fy + c = 0, find dy/dx.

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  18. If y = cos (m sin^(-1) x), prove that (1-x^2)y3 -3 xy2 + ( m^2 -1) y1=...

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  19. Differentiate tan^(-1)(2x/(1 - x^(2))) with respect to cos^(-1)((1 - x...

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  20. If y = sqrt((x-1)(x-2)(x-3)), find dy/dx.

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