Home
Class 11
MATHS
If e^(cot^(-1)x) Prove that (1+x^(2))y(2...

If `e^(cot^(-1)x)` Prove that `(1+x^(2))y_(2) +(2x + 1)y_(1) = 0`.

Text Solution

Verified by Experts

The correct Answer is:
`(1+x^(2))y_(2) +(2x + 1)y_(1) = 0`
Promotional Banner

Topper's Solved these Questions

  • DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 10.1|16 Videos

  • DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 10.2|20 Videos

  • COMBINATORICS AND MATHEMATICAL INDUCTION

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Choose the correct option for the following)|34 Videos

  • DIFFERENTIAL CALCULUS LIMITS AND CONTINUITY

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|58 Videos

Similar Questions

Explore conceptually related problems

If y=e^(tan^(-1)x) , show that (1+x^(2))y''+(2x-1)y'=0 .

If y=e^(tan^(-1)x) , show that (1+x^(2))y''+(2x-1)y'=0

(a) If y=cos(msin^(-1)x) prove that (1-x^(2))y_(3)-3xy_(2)+(m^(2)-1)y_(1)=0 (b) Find y'' if x^(4)+y^(4)=16 .

If y = sin (m sin^(-1) x), prove that (1 - x^2)y_2 -xy_1 + m^2 y = 0

If y = cos (m sin^(-1) x), prove that (1-x^2)y_3 -3 xy_2 + ( m^2 -1) y_1=0

If y=(cos^(-1)x)^(2) prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-2=0 . Hence find y_(2) when x=0

If y=(cos^(-1) x)^(2) prove that (1-x^(2)) (d^(2)y)/(dx^(2)) -x(dy)/(dx) -2=0 . Hence find y_(2) when x=0.

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

If y= (tan^(-1)x)^(2) , show that (x^(2)+1)^(2) y_(2)+2x(x^(2)+1)y_(1)=2 .

If y= (cos^(-1) x)^2 , prove that (1-x^2) (d^2y)/(dx^2) - x(dy)/(dx) -2 =0 , Hence find y_2 when x=0 .

PREMIERS PUBLISHERS-DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION -PROBLEMS FOR PRACTICE
  1. If e^(cot^(-1)x) Prove that (1+x^(2))y(2) +(2x + 1)y(1) = 0.

    Text Solution

    |

  2. If y = 1/root(3)(x)+log(5)x+8, find dy/dx.

    Text Solution

    |

  3. Differentiate log(e)x from first principles.

    Text Solution

    |

  4. y = a sinx log(10)x + e^(2x), find dy/dx.

    Text Solution

    |

  5. y = log sec(pi/4 + x/2), show that dy/dx=1/2tan(pi/4+x/2)

    Text Solution

    |

  6. If y = cos^(-1)((1-x)/(1+x)), show that dy/dx =1/(sqrt(x)(1+x))

    Text Solution

    |

  7. if y = x^(x^2), show that dy/dx = x^(x^(2))x(1+2logx)

    Text Solution

    |

  8. If y = x^(a)+a^(x)+x^(x)+a^(a), dind dy/dx.

    Text Solution

    |

  9. find dy/dx if y = (logx)^(sin^(-1)x

    Text Solution

    |

  10. f(x) = x^(x)+ x^(1/x), find f'(x).

    Text Solution

    |

  11. y = tan^(-1)((3x-x^(3))/(1-3x^(2))), find dy/dx.

    Text Solution

    |

  12. y = sec^(-1)((1+x^(2))/(1-x^(2))), find dy/dx.

    Text Solution

    |

  13. Find the derivatives of the following : tan^(-1)((cosx+sinx)/(cosx-s...

    Text Solution

    |

  14. If y = tan^(-1)((1+x^(2))/(1-x^(2))) Find dy/dx.

    Text Solution

    |

  15. y = tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(ax))), find dy/dx.

    Text Solution

    |

  16. y = tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))),find dy/dx.

    Text Solution

    |

  17. y = cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))),...

    Text Solution

    |

  18. Differentiate cosec^(-1)(1/(3x-4x^(3))):

    Text Solution

    |

  19. If x=asec^(3)theta " and " y=atan^(3)theta " find " (dy)/(dx) " at " t...

    Text Solution

    |

  20. If x = 2costheta- cos 2theta, y = 2sintheta -sin 2theta, find dy/dx.

    Text Solution

    |

  21. x = a(costheta + logtan(theta/2), y = asintheta, find dy/dx.

    Text Solution

    |