Home
Class 12
MATHS
If F(x) =f(x)phi(x) and f'(x)phi'(x)=a (...

If F(x) =f(x)`phi`(x) and f'(x)`phi'`(x)=a (a constant), then prove that ,`(F'')/F=(f'')/f+(phi'')/phi+(2a)/(fphi)`, where `''equivd^2/dx^2,'equivd/dx` and F(x)`ne`0.

Promotional Banner

Topper's Solved these Questions

  • SECOND ORDER DERIVATIVE

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Multiple correct answer type)|5 Videos

  • SECOND ORDER DERIVATIVE

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Integer answer type)|5 Videos

  • SECOND ORDER DERIVATIVE

    CHHAYA PUBLICATION|Exercise Short Answer type Question|50 Videos

  • REVISION OF PREVIOUS TWO DIMENSIONAL COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams E (Assertion - Reason Type )|2 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion-Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

If f(x) = |x-a| phi (x) , where phi(x) is continuous function, then

If f(x+2a)=f(x-2a) ,then prove that f(x) is periodic

If f(x)=int_a^x[f(x)]^(-1)dx and int_a^1[f(x)]^(-1)dx=sqrt(2) , then

inte^x(1+x)sec^2(xe^x)dx= f(x) +constant, then find f(x)

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

Let the question f(x) = logx^2 and phi(x) = 2 log x , then

If f(2a-x)=-f(x) then int_(0)^(2a)f(x)dx is equal to-

If f(x)+2f(1/x)=3x,x ne0 and S={x in RR:f(x)=f(-x)}, then S

If int f(x) dx=f(x) , then int {f(x)}^(2)dx is equal to -

If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a gt b gt 0) are constants, then prove that f(x) is a periodic function.

CHHAYA PUBLICATION-SECOND ORDER DERIVATIVE-Long answer type Question
  1. IF y=(cos^-1x)^2, prove that,(1-x^2)(d^2y)/(dx^2)-xdy/dx-2=0. Hence,...

    Text Solution

    |

  2. If y=e^x, Prove that , xy2-(2x-1)y1+(x-1)y=0.

    Text Solution

    |

  3. In the parabola y^2=4ax, prove that (d^2y)/(dx^2).(d^2x)/(dy^2)=(-2a)/...

    Text Solution

    |

  4. If x=cos t and y=log t , prove that at t=pi/2, (d^2y)/(dx^2)+(dy/dx)^2...

    Text Solution

    |

  5. IF x=t^2+2t,y=t^3-3t, where t is a parameter then show that, (d^2y)/(d...

    Text Solution

    |

  6. If y=ae^(tsqrt2)+be^(-tsqrt2) and x= sin t, show that, (1-x^2)(d^2y)...

    Text Solution

    |

  7. Evaluate int sin3x sin5xdx.

    Text Solution

    |

  8. If x=1/z and y=f(x), then prove that, (d^2f)/(dx^2)=2z^3dy/dz+z^4(d^...

    Text Solution

    |

  9. Putting logx=z show that, x^2(d^2y)/(dx^2)=(d^2y)/(dz^2)-dy/dz.

    Text Solution

    |

  10. If x=Ae^(-(kt)/2)cos(pt+in), and A,k,p,in are constants, show that (d^...

    Text Solution

    |

  11. IF y^4+5xy+y=2, find dy/dxand(d^2y)/(dx^2), when x=0,y=1.

    Text Solution

    |

  12. If F(x) =f(x)phi(x) and f'(x)phi'(x)=a (a constant), then prove that ,...

    Text Solution

    |

  13. IF y=e^(ax)sin bx, then prove that, (d^2y)/(dx^2)-2ady/dx+(a^2+b^2)...

    Text Solution

    |

  14. If y=cosecx+cotx, then show that,(d^2y)/(dx^2)=sinx/(1-cosx)^2.

    Text Solution

    |

  15. IF y^2=ax^2+2bx+c, Prove that (d^2x)/(dy^2)=(b^2-ac)/(ax+b)^3.

    Text Solution

    |

  16. IF y=Ae^(mx)+Be^(nx), show that y2-(m+n)y1+mny=0.

    Text Solution

    |

  17. IF xsqrt(1+y)+ysqrt(1+x)=0, show that, dy/dx=-1/(1+x)^2

    Text Solution

    |

  18. IF xsqrt(1+y)+ysqrt(1+x)=0, show that, (d^2y)/(dx^2)=2/(1+x)^3.

    Text Solution

    |

  19. IF y=e^(msin^-1x), find the value of (y2)0.

    Text Solution

    |

  20. IF y=sqrt(sin x+sqrt(sin x +sqrt(sin x +.... oo), show that (2y-1)^3...

    Text Solution

    |