Home
Class 12
MATHS
If y = tan^(-1)((5ax)/(a^2 - 6x^2)) . Pr...

If `y = tan^(-1)((5ax)/(a^2 - 6x^2))` . Prove that `(dy)/(dx) = (3a)/(a^2 + 9x^2) + (2a)/(a^2 + 4x^2)`

Text Solution

Verified by Experts

The correct Answer is:
`(2a)/(a^2 + 4x^2) + (3a)/(a^2 + 9x^2)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section VII)|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section VIII)|9 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section IV)|10 Videos

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )|45 Videos

Similar Questions

Explore conceptually related problems

If y = tan^-1 (4x)/(1+5x^2) + tan^-1(2+3x)/(3-2x) , prove that dy/dx = 5/(1+25x^2)

If y = (sin^-1x)/(sqrt(1-x^2)) , prove that (1-x^2)(dy/dx)- xy = 1

If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , prove that (dy)/(dx) = 4/(1 + x^2) , 0 < x < 1

If y = tan^-1((e^(2x) +1)/(e^(2x) -1)) , prove that : dy/dx =-(2e^(2x))/(1+e^4x)

If x^16 . y^9 = (x^2 + y)^(17) , prove that (dy)/(dx) = (2y)/x .

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

If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xdot

If y = tan x + sec x , prove that (d^2y)/(dx^2) = (cosx)/((1-sinx)^2)

If y = {x+sqrt (x^2 + a^2})^n , prove that dy/dx= (ny)/sqrt (x^2+a^2) .

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

BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES (Short Answer Type Questions)(Section V)
  1. Find (dy)/(dx) if x^3 + x^2y + xy^2 + y^3 = 81

    Text Solution

    |

  2. Find (dy)/(dx) when (x^2)/(a^2) + (y^2)/(b^2) = 2008.

    Text Solution

    |

  3. Find (dy)/(dx) , if sin^2 y + cos xy = pi

    Text Solution

    |

  4. Find (dy)/(dx), if sin^2 x + cos^2 y = 1

    Text Solution

    |

  5. If xsqrt(1 + y) + ysqrt(1 + x) = 0 show that (dy)/(dx) = - 1/(1 + x)^2

    Text Solution

    |

  6. If y = sqrt(log x + sqrt(logx + sqrt(log x + .....oo))) , prove that (...

    Text Solution

    |

  7. If cosy = xcos(a+y), with cos a ne +-1, prove that dy/dx = (cos^2(a+y...

    Text Solution

    |

  8. Differentiate sin^(-1) (xsqrt(x)) w.r.t.x.

    Text Solution

    |

  9. Differentiate tan^(-1)((sin x)/(1 + cos x)) w.r.t.x

    Text Solution

    |

  10. Find dy/dx when: y= cos^-1((1-x^2)/(1+x^2))

    Text Solution

    |

  11. Find dy/dx in the following:y=sec^-1(1/(2x^2-1)), 0ltxlt1/sqrt2

    Text Solution

    |

  12. Find (dy)/(dx), if y = tan^(-1) ((3x - x^3)/(1 - 3x^2)) , (-1)/(sqrt3)...

    Text Solution

    |

  13. Find (dy)/(dx), if y = tan^(-1) ((x^(1/3) + a^(1/3))/(1 - x^(1/3) a^(1...

    Text Solution

    |

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

    Text Solution

    |

  15. Differentiate tan^-1 (sqrt(1 + x^2) - x) w.r.t. x.

    Text Solution

    |

  16. Differentiate w.r.t x : cot^-1{(sqrt (1+sin x) + sqrt (1-sin x))/(sqrt...

    Text Solution

    |

  17. Differentiate tan^-1{( sqrt (1+x^2) +sqrt (1-x^2))/ (sqrt(1+x^2)-sqrt(...

    Text Solution

    |

  18. If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(d...

    Text Solution

    |

  19. If y = tan^(-1)((5ax)/(a^2 - 6x^2)) . Prove that (dy)/(dx) = (3a)/(a^2...

    Text Solution

    |

  20. If sqrt(1 - x^2) + sqrt(1 - y^2) = a (x - y) using inverse trignometri...

    Text Solution

    |