Home
Class 12
MATHS
If x=tan((1)/(2)logy), then show that (1...

If `x=tan((1)/(2)logy),` then show that `(1+x^(2))(d^(2)y)/(dx^(2))=(a-2x)(dy)/(dx).`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 1 MARK (TRUE OR FALSE QUESTIONS) TYPE-III|6 Videos

  • DIFFERENTAL QUATIONS

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 4 MARKS|41 Videos

  • INDEFINITE INTEGRALS

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 4 MARKS|15 Videos

Similar Questions

Explore conceptually related problems

If x = tan(1/a logy) , then show that (1+X^2) (d^2y)/(dx^2) + (2x -a) dy/dx = 0

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

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

(1+x^(2))(dy)/(dx)+y=e^(tan^(-1)x)

If y=e^(acos^(-1)3x) , prove that (1-9x^(2))(d^(2)y)/(dx^(2))-9x(dy)/(dx)-9a^(2)y=0 .

If y = e^(2tan^-1 x) , then show that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^2)dy/dx = 4y

If y = e^(3tan^-1 x) , then show that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^2)dy/dx = 9y

If y = e^(4tan^-1 x) , then show that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^2)dy/dx = 16y

ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. Differentiate the following with respect to x: sin^-1[(2^(x+1).3^x)/...

    Text Solution

    |

  2. If y=cos^(-1)((2^(x+1))/(1+4^(x))), find (dy)/(dx).

    Text Solution

    |

  3. If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , pr...

    Text Solution

    |

  4. If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(...

    Text Solution

    |

  5. If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))] find dy/dx

    Text Solution

    |

  6. Differentiate tan^(-1) ((sqrt(1 + x^2) - 1)/(x)) w.r.t. sin^(-1) ((2x...

    Text Solution

    |

  7. Differentiate tan^(-1)((sqrt(1 - x^2))/(x)) w.r.t. cos^(-1)(2x sqrt(1 ...

    Text Solution

    |

  8. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

    Text Solution

    |

  9. Find the derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2))...

    Text Solution

    |

  10. Find (dy)/(dx) when y=(sinx)^(x)+sin^(-1)sqrt(x).

    Text Solution

    |

  11. If y = 3 cos (log x) + 4 sin (log x) show that x^2 y2 + xy1 + y = 0

    Text Solution

    |

  12. If y=e^(ax)cosbx, then prove that (d^(2)y)/(dx^(2))-2a(dy)/(dx)+(a^(2)...

    Text Solution

    |

  13. If (a+bx)e^(y//x)=x, show that x^(3)y''=(xy'-y)^(2).

    Text Solution

    |

  14. If y=x^(3)log((1)/(x)), prove that (d^(2)y)/(dx^(2))-(2)/(x)(dy)/(dx)+...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If x^(p)y^(q)=(x+y)^(p+q), find (d^()y)/(dx^()).

    Text Solution

    |

  18. If y=log (x+ sqrt ( x^2+1)), prove that: (x^2+1) d^2y/dx^2 + xdy/dx=0.

    Text Solution

    |

  19. Find (d^2y)/(dx^2) in the following If x = a (theta + sin theta) , y...

    Text Solution

    |

  20. If x=acos theta+bsintheta and y=a sintheta-bcostheta, then prove that ...

    Text Solution

    |