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

Verified by Experts

`y=frac{a x+b}{x^{2}+c} `
` Rightarrow(x^{2}+c) y=a x+b`
Diffferentiating w.r.t. x we get
` 2 x y+(x^{2}+c) frac{d y}{d x}=a`
Diffferentiating w.r.t. x, 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=acos(lnx)+bsin(lnx) then prove that x^2y_3+3x y_2+2y_1=0

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

If y=x+(1)/(y) prove that (x^(2)-y^(2)+3)((dy)/(dx))=1

If y=e^acos^((-1)x) , then prove that (1-x^2)y_2-x y_1-a^2y=0 .

Three points A(x_1 , y_1), B (x_2, y_2) and C(x, y) are collinear. Prove that: (x-x_1) (y_2 - y_1) = (x_2 - x_1) (y-y_1) .

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 .

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_3y_2-y_3y_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 theta\ is the angle which the straight line joining the points (x_1, y_1)a n d\ (x_2, y_2) subtends at the origin, prove that tantheta=(x_2y_1-x_1y_2)/(x_1x_2+y_1y_2)\ a n dcostheta=(x_1x_2+y_1y_2)/(sqrt(x1 2+y1 2x2 2+y2 2))

If (x_1-x_2)^2+(y_1-y_2)^2=a^2,(x_2-x_3)^2+(y_2-y_3)^2=b^2 and (x_3-x_1)^2+(y_3-y_1)^2=c^2 then prove that 4|{:(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1):}|= (a+b+c)(b+c-a)(c+a-b)(a+b-c)

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y=a+b x^2,\ a ,\ b arbitrary constants, then (d^2y)/(dx^2)=2\ x y...

    Text Solution

    |

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

    Text Solution

    |

  3. If y=asinm x+bcosm x , then (d^2y)/(dx^2) is equal to (a)-m^2y (b) m^2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If y=acos((log)e x)+bsin((log)e x) , then x^2\ y2+x y1= (a) 0 (b) y (...

    Text Solution

    |

  8. If x=2at at y=a t^2 , where a is a constant, then (d^2y)/(dx^2) at x=1...

    Text Solution

    |

  9. If x=f(t) and y=g(t) , then (d^2y)/(dx^2) is equal to (f^(prime)g"-g'\...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...

    Text Solution

    |