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If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y), pro...

If `sqrt(1-x^2) + sqrt(1-y^2)=a(x-y)`, prove that `(dy)/(dx)= sqrt((1-y^2)/(1-x^2))`

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The correct Answer is:
`= sqrt((1-y^(2))/(1-x^(2)))`
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OSWAAL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-DIFFERENTIABILITY ( LONG ANSWER TYPE QUESTIONS-I)
  1. If y=logsqrt((1+tanx)/(1-tanx)),"P r o v et h a t"(dy)/(dx)=sec2x

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  2. If y = a sin x + b cos x, show that y^2+((dy)/(dx))^2=a^2+b^2

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  3. Consider the curve x= a(cos theta+theta sin theta) and y= a(sin theta ...

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  4. If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

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  5. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

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  6. If x=a\ (theta-sintheta),\ y=a\ (1+costheta),\ \ \ find (d^2\ y)/(dx^...

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  7. If y= log sqrt((1+x cos x)/(1- x cos x))," find "(dy)/(dx) in simplifi...

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  8. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), find the values of (dy)/(d...

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  9. Differentiate x^(xcosx)+(x^2+1)/(x^2-1) with respect to x :

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  10. If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .

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  11. If tan((x^2-y^2)/(x^2+y^2))=a then prove that (dy)/(dx)=y/x

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

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  13. Differentiate sin^(-1)((2x)/(1+x^(2))) w.r.t. cos^(-1)((1-x^(2))/(1+x^...

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  14. If y=(cot^(-1)x)^(2), then show that (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x...

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  15. Find (dy)/(dx), if y=sin^(-1)[xsqrt(\ 1-x)-\ sqrt(x)\ sqrt(1-x^2)\ ]\

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  16. Find dy/dx, if y=(cosx)^x+(sinx)^(1/x)

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  17. If y=e^a\ s in^((-1x))\ ,\ -1\ lt=x\ lt=1, then show that (1-x^2)\...

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  18. If y=cos^(-1)((3x+4\ sqrt(1-x^2))/5),\ "f i n d"(dy)/(dx)

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  19. If y="c o s e c"^(-1)x ,\ \ x >1 , then show that x(x^2-1)(d^2y)/(dx^2...

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  20. If y=(sinx-cosx)^(sinx-cosx),pi/4<x<(3pi)/4,"f i n d"(dy)/(dx)dot

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