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If y=sin^(-1)x, show that (1-x^2)(d^2y)/...

If `y=sin^(-1)x`, show that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0`.

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OSWAAL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-DIFFERENTIABILITY ( LONG ANSWER TYPE QUESTIONS-I)
  1. If y=(t a n^(-1)\ x^2) , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...

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  2. If y=3cos(logx)+4sin(logx),\ then show that x^2dot(d^2\ y)/(dx^2)+...

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  3. If y=sin^(-1)x, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0.

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  4. Differentiate tan^(-1)[(sqrt(1+x^2)-1)/x] with respect to x

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  5. If x=a(cos t+t\ s in\ t) and y=a\ (sint-t\ cos t),\ \ then find (d^2\...

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

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  7. If y=(sin^(-1)x)/(sqrt(1-x^2)) , show that (1-x^2)(d^2y)/(dx^2)-3x(dy)...

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  8. If x=a(theta-sintheta) and, y=a(1+costheta) , find (dy)/(dx) at theta=...

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  9. If y=logsqrt((1+tanx)/(1-tanx)),"P r o v et h a t"(dy)/(dx)=sec2x

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

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

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

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

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

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

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

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

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

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

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