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If siny=x sin(a+y), prove that, (dy)/(dx...

If `siny=x sin(a+y)`, prove that, `(dy)/(dx)=(sin a)/(1-2x cos a +x^(2))`.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(d) (SHORT ANSWER TYPE QUESTIONS)
  1. Find the derivative of y w.r.t. x in each of the following : y/(x+y)...

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  2. Find the derivatives of f(x) w.r.t. x in the following : f(x)=root(3...

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  3. Find the derivatives of f(x) w.r.t. x in the following : f(x)=root(3...

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  4. Find the derivatives of f(x) w.r.t. x in the following : f(x)=(x^(2)...

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  5. Find the derivatives of f(x) w.r.t. x in the following : g(x)=root(3...

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  6. Obtain dy/dx when : x^(2)+y^(2)+2axy = 0

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  7. Find dy/dx if x^(3)+y^(3)-3axy=0.

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  8. If x^(2)+y^(2)+2gx+2fy+c=0 then (dy)/(dx)=

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  9. Obtain dy/dx when : x^(4)+y^(4)+4xy-100 = 0

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  10. If ax^2+2hxy+by^2=0 then (dy)/(dx)=

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  11. If sqrtx+sqrty=5,"find "dy/dx at (4, 9).

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  12. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

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  13. If y =sqrtx +(1)/(sqrtx), then the value of (2x (dy)/(dx)+y) is-

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  14. Find dy/dx for each of the following y=(x^(2)+3x+5)(x^(2)-2)^(2)

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  15. Find dy/dx for each of the following y=(sqrtx+1/sqrtx)(1+x+x^(2))

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  16. Find dy/dx for each of the following y=((x-sqrtx)/(1-2x))^(2)

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  17. Find dy/dx for each of the following y=(1/(1+x))(x^(-2)+2/x-1)+root(...

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  18. Find dy/dx for each of the following y=root(3)(x^(2)(x^(2)+3)).

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  19. If cosy=xcos(a+y), with cosa!=+-1, prove that (dy)/(dx)=(cos^2(a+y))/(...

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

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