Home
Class 12
MATHS
If y=(a x+b)/(x^2+c), prove that (2x y1+...

If `y=(a x+b)/(x^2+c),` prove that `(2x y_1+y)y_3=3(x y_2+y_1)y_2.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|406 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

If y=(a x+b)/(x^2+c), then (2x y_1+y) y_3=

If y=(sin^(-1)x)^2 , prove that (1-x^2)y_2-x y_1-2=0 .

If y=(sin^(-1)x)^2 ,prove that (1-x^2)y_2-x y_1-2=0.

If y=(tan^(-1)x)^2 , then prove that (1+x^2)^2\ y_2+2x\ (1+x^2)y_1=2 .

If y=(cot^(-1)x)^2 , prove that y_2(x^2+1)^2+2x(x^2+1)y_1=2 .

If y=log (1+ sin x), prove that y_(4)+y_(3)y_(1)+y_(2)^(2)=0 .

If y=log (1+ sin x), prove that y_(4)+y_(3)y_(1)+y_(2)^(2)=0 .

y=[log(x+sqrt(x^2+1))]^2 then prove that (x^2+1)y_2+x y_1=2

A triangle has vertices A_i(x_i , y_i)fori=1,2,3 If the orthocentre of triangle is (0,0), then prove that |x_2-x_3 y_2-y_3 y_1(y_2-y_3)+x_1(x_2-x_3) x_3-x_1y_2-y_3y_2(y_3-y_1)+x_1(x_3-x_1) x_1-x_2y_2-y_3y_3(y_1-y_2)+x_1(x_1-x_2)|=0

If the tangent at (x_1,y_1) to the curve x^3+y^3=a^3 meets the curve again in (x_2,y_2), then prove that (x_2)/(x_1)+(y_2)/(y_1)=-1

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)ddot(cosn x+isinn x) a...

    Text Solution

    |

  2. If y=asinm x+bcosm x , then find dy/dx

    Text Solution

    |

  3. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (...

    Text Solution

    |

  4. If y=tan^(-1){((log)e(e//x^2))/((log)e(e x^2))}+tan^(-1)((3+2\ (log)e ...

    Text Solution

    |

  5. Let f(x) be a polynomial. Then, the second order derivative of f(e^...

    Text Solution

    |

  6. If y=acos((log x)+bsin((log x) , then find dy/dx

    Text Solution

    |

  7. If x=2 and y=a t^2 ,then find dy/dx

    Text Solution

    |

  8. If x=f(t) and y=g(t) , then find (dy)/(dx)

    Text Solution

    |

  9. If y=sin(m\ sin^(-1)x) , then (1-x^2)y2-x y1 is equal to m^2y (b) m y ...

    Text Solution

    |

  10. If y=(sin^(-1)x)^2,\ then (1-x^2)y2 is equal to x y1+2 (b) x y1-2 (c)...

    Text Solution

    |

  11. If y=e^(tanx) , then (cos^2x)y2-(1+sin2x)y1=0

    Text Solution

    |

  12. If y=2/(sqrt(a^2-b^2)){tan^(-1)sqrt((a-b)/(a+b))tan(x/2)} , then show ...

    Text Solution

    |

  13. If y=(a x+b)/(x^2+c), prove that (2x y1+y)y3=3(x y2+y1)y2.

    Text Solution

    |

  14. If y=loge(x/(a+b x))^x , then x^3y2 is (a) (x y1-y)^2 (b) (1+y)^2 ...

    Text Solution

    |

  15. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

    Text Solution

    |

  16. If y^(1/n)+y^(-1/n) = 2x then (x^2-1)y2+xy1 is equal to

    Text Solution

    |

  17. differentiate y= sinx +logx with respect to x

    Text Solution

    |

  18. If y=xlogx then find dy/dx

    Text Solution

    |

  19. find dy/dx if x y-(log y)=1

    Text Solution

    |

  20. If y^2=a x^2+b x+c , then find (dy)/(dx)

    Text Solution

    |