Home
Class 12
MATHS
Differentiate log(x+sqrt(a^2+x^2)) with ...

Differentiate `log(x+sqrt(a^2+x^2))` with respect to `x` .

Text Solution

AI Generated Solution

To differentiate the function \( y = \log(x + \sqrt{a^2 + x^2}) \) with respect to \( x \), we can follow these steps: ### Step 1: Identify the function We have: \[ y = \log(x + \sqrt{a^2 + x^2}) \] ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

Differentiate log(x+sqrt(x^(2)+1)) with respect to x:

Differentiate y=log(x+sqrt(x^2+1))

Differentiate e^(x)log sqrt(x)tan x with respect to x

Differentiate log sqrt((x-1)/(x+1)) with respect to x:

Differentiate log{x+2+sqrt(x^(2)+4x+1)} with respect to x:

Differentiate (e^(x)log x)/(x^(2)) with respect to x:

Differentiate log(cos x^(2)) with respect to x:

Differentiate log(sec x+tan x) with respect to x:

Differentiate log((sin x)/(1+cos x)) with respect to x:

Differentiate: (log x)^(x)+x^(log x) with respect to x:

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate logtan(pi/4+x/2) with respect to x :

    Text Solution

    |

  2. Differentiate sqrt(log{sin((x^2)/3-1)}) with respect to x

    Text Solution

    |

  3. Differentiate log(x+sqrt(a^2+x^2)) with respect to x .

    Text Solution

    |

  4. Differentiate log{(a+bsinx)/(a-bsinx)} with respect to x .

    Text Solution

    |

  5. Differentiate (e^x+e^(-x))/(e^x-e^(-x)) with respect to x .

    Text Solution

    |

  6. Differentiate logsqrt((1+sinx)/(1-sinx)) with respect to x .

    Text Solution

    |

  7. Find (dy)/(dx) , when y=e^(a x)cos(b x+c)

    Text Solution

    |

  8. Find (dy)/(dx) , when y=(e^x+logx)/(sin3x)

    Text Solution

    |

  9. Find (dy)/(dx) , when y=e^xlog(1+x^2)

    Text Solution

    |

  10. Find (dy)/(dx) , when y=(sinx+x^2)/(cot2x)

    Text Solution

    |

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

    Text Solution

    |

  12. If y=(xsin^(-1)x)/(sqrt(1-x^2))+logsqrt(1-x^2) , then prove that (dy)...

    Text Solution

    |

  13. Differentiate sin(m\ sin^(-1)x) with respect to x :

    Text Solution

    |

  14. Differentiate (a^(sin^(-1)x))^2 with respect to x :

    Text Solution

    |

  15. Differentiate: e^(cos^(-1)sqrt(1-x^(2))

    Text Solution

    |

  16. Differentiate (log)(10)x+(log)x 10+(log)(x) x+(log)(10)10 with respect...

    Text Solution

    |

  17. Differentiate 5^3-x^2+(3-x^2)^5 with respect to x :

    Text Solution

    |

  18. If y=(sqrt(a^2+x^2)+sqrt(a^2-x^2))/(sqrt(a^2+x^2)-sqrt(a^2-x^2)), show...

    Text Solution

    |

  19. If y=sqrt((1-x)/(1+x)), find (dy)/(dx) and prove that (1-x^2)(dy)/(dx)...

    Text Solution

    |

  20. If y=sqrt((1+e^x)/(1-e^x)),s howt h a t(dy)/(dx)=(e^x)/((1-e^x)sqrt(1...

    Text Solution

    |