Home
Class 12
MATHS
If y=tanx , prove that y2=2y y1 ....

If `y=tanx` , prove that `y_2=2y y_1` .

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=e^(tan^-1x), prove that (1+x^2)y_2+(2x-1)y_1=0

If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

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

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

If y=secx+tanx then prove that (d^2y)/(dx^(2))=cosx/((1-sinx)^(2)) .

If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

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 .

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

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

RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=Acos(logx)+\ Bsin(logx) , prove that x^2\ (d^2y)/(dx^2)+x(dy)/(dx...

    Text Solution

    |

  2. If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

    Text Solution

    |

  3. If y=tanx , prove that y2=2y y1 .

    Text Solution

    |

  4. If y=tan^(-1)x , find (d^2y)/(dx^2) in terms of y alone.

    Text Solution

    |

  5. If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

    Text Solution

    |

  6. If y^3-y=2x , prove that (d^2y)/(dx^2)=-(24 y)/((3y^2-1)^3) .

    Text Solution

    |

  7. If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

    Text Solution

    |

  8. If y=x^x , find (d^2y)/(dx^2) .

    Text Solution

    |

  9. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

    Text Solution

    |

  10. If y=log{x+ sqrt( x^2+a^2 )} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy...

    Text Solution

    |

  11. If y=sin^(-1)x , then show that (1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0 .

    Text Solution

    |

  12. If y=e^m\ sin^((-1)x) , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2...

    Text Solution

    |

  13. If y={x+sqrt(x^2+1)}^m , show that (x^2+1)y2+x y1-m^2\ y=0

    Text Solution

    |

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

    Text Solution

    |

  15. If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .

    Text Solution

    |

  16. If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

    Text Solution

    |

  17. Find (d^2y)/(dx^2) , if x=a t^2,\ \ y=2a t .

    Text Solution

    |

  18. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

    Text Solution

    |

  19. If x=asint and y=a(cost+log tan(t/2) ) , find (d^2y)/(dx^2) .

    Text Solution

    |

  20. lf x=acostheta+bsintheta, y=asintheta-bcostheta then show that y^2(d^...

    Text Solution

    |