Home
Class 12
MATHS
If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+...

If `y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a))`, then prove that `(dy)/(dx)=(2a^(3))/(x^(4)-a^(4))`.

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (1 MARK)|8 Videos

  • CHSE ODISHA EXAMINATION PAPER 2020

    ARIHANT PUBLICATION|Exercise GROUP C (ANSWER ANY ONE QUESTIONS)|11 Videos

  • DETERMINANTS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE |39 Videos

Similar Questions

Explore conceptually related problems

If (x)/(x-y)=log((a)/(x-y)) , then prove that (dy)/(dx)=2-(x)/(y) .

If y=(x)/(x+2) then prove that x(dy)/(dx)=(1-y)y .

If (x-y)*e^((x)/(x-y))=a , then prove that y(dy)/(dx)+x=2y .

If y =x log (x/(a+bx)) then prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2 .

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

If y=[x+sqrt(x^(2)+a^(2))]^(n) , then prove that (dy)/(dx)=(ny)/(sqrt(x^(2)+a^(2)))

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

ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -CHAPTER PRACTICE (4 MARK)
  1. Find the derivative of (x+sinx)/(x+cosx) w.r.t. x.

    Text Solution

    |

  2. Differentiate w.r.t. x, sin^(-1)[(2^(x+1)*3^(x))/(1+(36)^(x))].

    Text Solution

    |

  3. If y=(sin(ax+b))/(cos(cx+d)), the find (dy)/(dx).

    Text Solution

    |

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

    Text Solution

    |

  5. If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a)), then prove that (dy)/(dx)...

    Text Solution

    |

  6. If x=a((1-t^(2))/(1+t^(2))) and y=(2t)/(1-t^(2)), then find (dy)/(dx).

    Text Solution

    |

  7. If x=a(costheta+log"tan"(theta)/(2)) and y=asin theta, then find the v...

    Text Solution

    |

  8. Differentiate x^(xcosx)+(x^(2)+1)/(x^(2)-1) w.r.t. x.

    Text Solution

    |

  9. If y=(sin x - cos x)^((sinx-cosx)),(pi)/(4)ltxlt(3pi)/(4), then find (...

    Text Solution

    |

  10. If log(sqrt(1+x^(2))-x)=ysqrt(1+x^(2)), then show that (1+x^(2))(dy)/(...

    Text Solution

    |

  11. Discuss the continuity of secant.

    Text Solution

    |

  12. Find the set of points, where the function f given by f(x)=|2x-1|sin x...

    Text Solution

    |

  13. If y=e^(x)sinx, then prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0,

    Text Solution

    |

  14. Find (dy)/(dx), where y=x^(cotx)+(2x^(2)-3)/(x^(2)+x+2).

    Text Solution

    |

  15. Find the derivative of (sinx)^(x)+sinsqrt(x) w.r.t. x.

    Text Solution

    |

  16. For what value of lamda the function defined by f(x)={{:(lamda(x^(2)+2...

    Text Solution

    |

  17. Find the value of k, the function, f(x)={:{((1-sinx)/((pi-2x)^(2))",...

    Text Solution

    |

  18. If y=(sin^(-1)x)/(sqrt(1-x^(2))), the prove that (1-x^(2))(d^(2)y)/(dx...

    Text Solution

    |

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

    Text Solution

    |

  20. If y=(x+(1)/(x+(1)/(x+ . . .oo))) find (dy)/(dx), the rhs being a vali...

    Text Solution

    |