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Find dy/dx for each of the following: ...

Find `dy/dx` for each of the following:
`y=(sqrtx+1/sqrtx)(1+x+x^2)`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If y=sqrtx+1/(sqrtx), then show that 2x(dy)/(dx)+y = 2√ x

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  2. Find dy/dx for each of the following: y = (x^2+3x+5)(x^2-2)^2

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  3. Find dy/dx for each of the following: y=(sqrtx+1/sqrtx)(1+x+x^2)

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  4. Find dy/dx for each of the following: y=((x-sqrtx)/(1-2x))^2

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  5. Find dy/dx for each of the following: y=(1/(1+x))(x^-2+2/x-1)+root3(...

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  6. Find dy/dx for each of the following: y=root3(x^2(x^2+3))

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  7. If cosy = xcos(a+y), with cos a ne +-1, prove that dy/dx = (cos^2(a+y...

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  8. If sin y = x sin (a+y), then show that: dy/dx=(sina)/(1-2xcosa+x^2)

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  9. Differentiate the following w.r.t. x: tan^-1sqrtx

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  10. Differentiate the following w.r.t. x: cos^-1(x/(x+1))

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  11. Differentiate the following w.r.t. x: sin^-1(xsqrtx),0lexle1

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  12. Differentiate the following w.r.t. x: (tan^-1x)^2

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  13. Differentiate the following w.r.t. x: x sec^-1x

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  14. Differentiate the following w.r.t.x. cos^(-1) (sin x)

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  15. Differentiate the following w.r.t. x: tan(sin^-1x)

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  16. Differentiate the following w.r.t. x: sin^-1(2x)

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  17. Differentiate the following w.r.t. x: (cot^-1x)^2

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  18. Differentiate the following w.r.t. x: sin(2 sin^-1x)

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  19. Differentiate the following w.r.t. x: x tan^-1x

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  20. Differentiate the following w.r.t. x: tan^-1((sinx)/(1+cosx))

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