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If xsqrt(1+y) + ysqrt(1+x) = 0 for x lie...

If `xsqrt(1+y) + ysqrt(1+x) = 0` for x lies between -1 and 1` prove that dy/dx =-1/(1+x)^2

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Obtain dy/dx when: x^2+y^2+2gx+2fy+c=0

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  2. Obtain dy/dx when: x^4+y^4+4xy-100=0

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  3. If xsqrt(1+y) + ysqrt(1+x) = 0 for x lies between -1 and 1 prove that ...

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  4. If y=sqrtx+1/(sqrtx), then show that 2x(dy)/(dx)+y = 2√ x

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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