Home
Class 11
MATHS
If f(x)=(x^(3))/(a^(2)-x^(2)) then find ...

If `f(x)=(x^(3))/(a^(2)-x^(2))` then find the value of `f'((a)/(2))`.

Text Solution

AI Generated Solution

To find the derivative \( f' \left( \frac{a}{2} \right) \) for the function \( f(x) = \frac{x^3}{a^2 - x^2} \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), then its derivative is given by: \[ f'(x) = \frac{u'v - uv'}{v^2} \] where \( u = x^3 \) and \( v = a^2 - x^2 \). ...
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN|Exercise EX-13A|52 Videos
  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN|Exercise EX-13B|11 Videos
  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|6 Videos
  • LINEAR INEQUALITIES

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|14 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^3+2x then find the value of f(4)

IF f(x)=2x^(3)+3x^(2)+5 , then find the value of f(2) .

g(x) is a inverse function of f.g(x)=x^(3)+e^((x)/(2)) then find the value of f'(x)

If f(x)=2x^(3)-13x^(2)+17x+12 , then find the value of f(-2) and f(3).

If f(x)=x^(3)+2x , then find the value of f(3) .

If f'(x)=(1)/(x)+x^(2) and f(1)=(4)/(3) then find the value of f(x)

If f(x)=x^(2) then the value of f+3 is

" (1) If "f(x+(1)/(x))=x^(2)+(1)/(x^(2))(x!=0);" then find the value of "f(x)

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

NAGEEN PRAKASHAN-LIMITS AND DERIVATIVES-Miscellaneous Exercise
  1. If f(x)=(x^(3))/(a^(2)-x^(2)) then find the value of f'((a)/(2)).

    Text Solution

    |

  2. Find the derivative of the following functions from first principles:...

    Text Solution

    |

  3. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  4. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  5. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  6. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  7. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  8. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  9. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  10. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  11. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  12. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  13. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  14. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  15. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  16. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  17. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  18. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  19. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  20. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |

  21. Find the derivative of the following functions (it is to be understand...

    Text Solution

    |