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If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqr...

If `y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) `, show that `(dy)/(dx) - (2x)/(sqrt(1 - x^4)) = 1/(sqrt(1 - x^2))`

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The correct Answer is:
`1/(sqrt(1 - x^2))`
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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES (Short Answer Type Questions)(Section V)
  1. Find (dy)/(dx) if x^3 + x^2y + xy^2 + y^3 = 81

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  2. Find (dy)/(dx) when (x^2)/(a^2) + (y^2)/(b^2) = 2008.

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  3. Find (dy)/(dx) , if sin^2 y + cos xy = pi

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  4. Find (dy)/(dx), if sin^2 x + cos^2 y = 1

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  5. If xsqrt(1 + y) + ysqrt(1 + x) = 0 show that (dy)/(dx) = - 1/(1 + x)^2

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  6. If y = sqrt(log x + sqrt(logx + sqrt(log x + .....oo))) , prove that (...

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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. Differentiate sin^(-1) (xsqrt(x)) w.r.t.x.

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  9. Differentiate tan^(-1)((sin x)/(1 + cos x)) w.r.t.x

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  10. Find dy/dx when: y= cos^-1((1-x^2)/(1+x^2))

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  11. Find dy/dx in the following:y=sec^-1(1/(2x^2-1)), 0ltxlt1/sqrt2

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  12. Find (dy)/(dx), if y = tan^(-1) ((3x - x^3)/(1 - 3x^2)) , (-1)/(sqrt3)...

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  13. Find (dy)/(dx), if y = tan^(-1) ((x^(1/3) + a^(1/3))/(1 - x^(1/3) a^(1...

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  14. Differentiate tan^(-1) ((sqrt(1 + x^2) - 1)/(x)) w.r.t.x .

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  15. Differentiate tan^-1 (sqrt(1 + x^2) - x) w.r.t. x.

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  16. Differentiate w.r.t x : cot^-1{(sqrt (1+sin x) + sqrt (1-sin x))/(sqrt...

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  17. Differentiate tan^-1{( sqrt (1+x^2) +sqrt (1-x^2))/ (sqrt(1+x^2)-sqrt(...

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  18. If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(d...

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  19. If y = tan^(-1)((5ax)/(a^2 - 6x^2)) . Prove that (dy)/(dx) = (3a)/(a^2...

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  20. If sqrt(1 - x^2) + sqrt(1 - y^2) = a (x - y) using inverse trignometri...

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