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If y=sqrt(x+1)-sqrt(x-1), prove that (x^...

If `y=sqrt(x+1)-sqrt(x-1)`, prove that `(x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx)-(1)/(4)y=0`.

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ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. If y = {x+sqrt (x^2 + a^2})^n, prove that dy/dx= (ny)/sqrt (x^2+a^2).

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  2. If (x)/(x-y)="log"(a)/(x-y), then prove that (dy)/(dx)=2-(x)/(y).

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

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  4. If f(x)=sqrt(x^(2)+1),g(x)=(x+1)/(x^(2)+1) and h(x)=2x-3, then find f'...

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  5. IF [x= a {(1 + t^2) /(1-t^2)] and [y= 2t/(1 -t^2)] find dy/dx.

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  6. Differentiate 7x^(5)-11x^(2) w.r.t. 7x^(2)-15x.

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  7. If x^(2)+y^(2)=t-(1)/(t) and x^(4)+y^(4)=t^(2)+(1)/(t^(2)), show that ...

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  8. If ysqrt(x^(2)+1)=log(x+sqrt(x^(2)+1)), show that (x^(2)+1)(dy)/(dx)+x...

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  9. If e^(x)+e^(y)=e^(x+y), prove that (dy)/(dx)+e^(y-x)=0.

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  10. If xsqrt(1+y+)ysqrt(1+x)=0 then (dy)/(dx) equals.

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  11. If y=x^(e^(x^(2))), find (dy)/(dx).

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  12. If x^(y)=e^(x-y), then prove that (dy)/(dx)=(logx)/((1+logx)^(2))

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  13. Differentiate the following w.r.t.x. If y^x = e^(y - x), prove that ...

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  14. If x^p . y^q = (x + y)^(p + q) , show that (dy)/(dx) = y/x

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  15. If x^16 . y^9 = (x^2 + y)^(17), prove that (dy)/(dx) = (2y)/x.

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  16. Find (dy)/(dx), if y^(x) + x^(y) +x^(x) = a^(b).

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  17. If y=asinx+bcosx, prove thaty^2+((dy)/(dx))^2=a^2+b^2

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  18. If x sin (a+y) + sin a cos (a+y) = 0, then prove that : dy/dx = (sin^...

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  19. Find the value of (dy)/(dx) at theta=(pi)/(4) if x=ae^(theta)(sintheta...

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  20. If x=cost(3-2cos^(2)t) and y=sint(3-2sin^(2)t), find the value of (dy)...

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