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if cos(xy)=x, show that (dy)/(dx)=(-(1+y...

if cos(xy)=x, show that `(dy)/(dx)=(-(1+ysin(xy)))/(xsinxy)`.

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SURA PUBLICATION-DIFFERENTIAL CALCUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION-EXERCISE 10.4
  1. Find the derivatives of the following : sqrt(x^(2)+y^(2))=tan^(-1)(y...

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  2. Find the derivatives of the following : tan(x+y)+tan(x-y)=x

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  3. if cos(xy)=x, show that (dy)/(dx)=(-(1+ysin(xy)))/(xsinxy).

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  4. Find the derivatives of the following : tan^(-1)sqrt((1-cosx)/(1+cos...

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  5. Find the derivatives of the following : tan^(-1)((6x)/(1-9x^(2)))

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  6. Find the derivatives of the following : cos(2tan^(-1)sqrt((1-x)/(1+x...

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  7. Find the derivatives of the following : x=acos^(3)t, y=asin^(3)t

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  8. Find the derivatives of the following : x=a(cost+tsint), y=a(sint-tc...

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  9. Find the derivatives of the following : x=(1-t^(2))/(1+t^(2)), y=(2t...

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  10. Find the derivatives of the following : cos^(-1)((1-x^(2))/(1+x^(2))...

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  11. Find the derivatives of the following : sin^(-1)(3x-4x^(3))

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  12. Find the derivatives of the following : tan^(-1)((cosx+sinx)/(cosx-s...

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  13. Find the derivative of sinx^(2) with respect to x^(2).

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  14. Find the derivative of sin^(-1)((2x)/(1+x^(2))) with respect to tan^(-...

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  15. If u=tan^(-1)""(sqrt(1+x^(2))-1)/x " and " v=tan^(-1)x, " find " (du)/...

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  16. Find the derivative with tan^(-1)(sinx/(1+cosx)) with respect to tan^(...

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  17. If y=sin^(-1)x then find y''.

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  18. If y=e^(tan^(-1)x), show that (1+x^(2))y''+(2x-1)y'=0.

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  19. If y=sin^(-1)x/sqrt(1-x^(2)) show that (1-x^(2))y(2)-3xy(1)-y=0.

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  20. If x=a(theta+sintheta), y=a(1-costheta) then prove that at theta=pi/2,...

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