Home
Class 12
MATHS
If y=(a x+b)/(x^2+c), then (2x y1+y) y3=...

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

Text Solution

Verified by Experts

Given
`y=(a x+b)/(x^2+c)`
=`(x^2+c)y=(ax+b)`
differentiating both side we get
=`(x^2+c)y_1 +2xy=(a)`
or,`y_1=(a-2xy)/(x^2+c)`
again differentiating both side we get
...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If y=(ax+b)/(x^(2)+c), prove that (2xy_(1)+y)y_(3)=3(xy_(2)+y_(1))y_(2)

If y=(log)_(e)((x)/(a+bx))^(x), then x^(3)y_(2)=(xy_(1)-y)^(2)(b)(1+y)^(2)(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

If cos x+cos y-cos(x+y)=(3)/(2), then (a) x+y=0( b) x=2y( c) x=y( d )2x=y

If A(x_1, y_1), B (x_2, y_2) and C (x_3, y_3) are the vertices of a DeltaABC and (x, y) be a point on the internal bisector of angle A , then prove that : b|(x,y,1),(x_1, y_1, 1), (x_2, y_2, 1)|+c|(x, y,1), (x_1, y_1, 1), (x_3, y_3, 1)|=0 where AC = b and AB=c .

If A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4

If the circle x^2 + y^2 = a^2 intersects the hyperbola xy=c^2 in four points P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4) , then : (A) x_1 + x_2 + x_3 + x_4 = 0 (B) y_1 + y_2 + y_3 + y_4 = 0 (C) x_1 x_2 x_3 x_4= c^4 (D) y_1 y_2 y_3 y_4 = c^4

If the points (x_1, y_1), (x_2, y_2) and (x_3, y_3) be collinear, show that: (y_2 - y_3)/(x_2 x_3) + (y_3 - y_1)/(x_3 x_2) + (y_1 - y_2)/(x_1 x_2) = 0

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0

    Text Solution

    |

  2. If y=tanx+secx ,p rov et h a t(d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

    Text Solution

    |

  3. If y=(a x+b)/(x^2+c), then (2x y1+y) y3=

    Text Solution

    |

  4. If y=(log)e(x/a)^x ,then x^3y2=

    Text Solution

    |

  5. If sin^(-1) (1 – x) – 2sin^(-1) x = π / 2,then x is equal to

    Text Solution

    |

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

    Text Solution

    |

  7. If y=x^(n-1)lnx then x^2y2+(3-2n)x y1 is equal to -(n-1)^2y (b) (n...

    Text Solution

    |

  8. If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...

    Text Solution

    |

  9. If x=f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h ...

    Text Solution

    |

  10. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

    Text Solution

    |

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

    Text Solution

    |

  12. If y=tan^-1((log(e/x^2))/(log(ex^2)))+tan^-1((3+2logx)/(1-6logx)), the...

    Text Solution

    |

  13. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)fx-xy(x)= 1 (b) -1...

    Text Solution

    |

  14. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosn x+isinn x)...

    Text Solution

    |

  15. (d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...

    Text Solution

    |

  16. If x=acosn t-bsinn t ,t h e n(d^2x)/(dt^2) is n^2x (b) -n^2x (c) -n ...

    Text Solution

    |

  17. In (dy)/(dx),x is a independent variable and y is the dependent vari...

    Text Solution

    |

  18. If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...

    Text Solution

    |

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

    Text Solution

    |

  20. If y=Acosn x+Bsinn x , show that (d^2y)/(dx^2)+n^2\ y=0 .

    Text Solution

    |