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If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1...

If `y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))]` find `dy/dx`

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Verified by Experts

The correct Answer is:
`(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x)sqrt(1-x))`.
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ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. Differentiate the following with respect to x: sin^-1[(2^(x+1).3^x)/...

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  2. If y=cos^(-1)((2^(x+1))/(1+4^(x))), find (dy)/(dx).

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  3. If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , pr...

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  4. If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(...

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  5. If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))] find dy/dx

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

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  7. Differentiate tan^(-1)((sqrt(1 - x^2))/(x)) w.r.t. cos^(-1)(2x sqrt(1 ...

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  8. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  9. Find the derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2))...

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  10. Find (dy)/(dx) when y=(sinx)^(x)+sin^(-1)sqrt(x).

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  11. If y = 3 cos (log x) + 4 sin (log x) show that x^2 y2 + xy1 + y = 0

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  12. If y=e^(ax)cosbx, then prove that (d^(2)y)/(dx^(2))-2a(dy)/(dx)+(a^(2)...

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  13. If (a+bx)e^(y//x)=x, show that x^(3)y''=(xy'-y)^(2).

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  14. If y=x^(3)log((1)/(x)), prove that (d^(2)y)/(dx^(2))-(2)/(x)(dy)/(dx)+...

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  15. If x=tan((1)/(2)logy), then show that (1+x^(2))(d^(2)y)/(dx^(2))=(a-2x...

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  16. If y=x^(x), prove that (d^(2)y)/(dx^(2))-(1)/(y)((dy)/(dx))^(2)-(y)/(x...

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  17. If x^(p)y^(q)=(x+y)^(p+q), find (d^()y)/(dx^()).

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  18. If y=log (x+ sqrt ( x^2+1)), prove that: (x^2+1) d^2y/dx^2 + xdy/dx=0.

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  19. Find (d^2y)/(dx^2) in the following If x = a (theta + sin theta) , y...

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  20. If x=acos theta+bsintheta and y=a sintheta-bcostheta, then prove that ...

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