Home
Class 12
MATHS
Differentiate sin^(-1)(x/(sqrt(x^2+a^2))...

Differentiate `sin^(-1)(x/(sqrt(x^2+a^2)))` with respect to `x` :

Text Solution

AI Generated Solution

To differentiate \( \sin^{-1} \left( \frac{x}{\sqrt{x^2 + a^2}} \right) \) with respect to \( x \), follow these steps: ### Step-by-Step Solution: 1. **Let \( u = \sin^{-1} \left( \frac{x}{\sqrt{x^2 + a^2}} \right) \).** 2. **Substitute \( x = a \tan \theta \):** \[ ...
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 sin^(-1)((1)/(sqrt(1+x^(2)))) with respect to x

Differentiate sin ^(-1) (1/sqrt(1+x^2)) with respect to 'x'

Differentiate sin^(-1)(2x sqrt(1-x^(2))) with respect to x, if '1/(sqrt(2))

Differentiate sin^(-1)(2x sqrt(1-x^(2))) with respect to x, if ^(*)-1/(sqrt(2))

Differentiate sin^(-1)(2x sqrt(1-x^(2))) with respect to x, if '-1

Differentiate sin^(-1)(2ax sqrt(1-a^(2)x^(2))) with respect to sqrt(1-a^(2)x^(2)), if -1/(sqrt(2))

Differentiate sin^(-1)sqrt(1-x^(2)) with respect to if 0

Differentiate sin ^(-1)(2x sqrt(1-x^2)) with respect to sin^-1 x.

Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) with respect to sin^(-1)(2x sqrt(1-x^(2))), if -(1)/(sqrt(2))

Differentiate sin^(-1)(2x sqrt(1-x^(2))) with respect to sec^(-1)((1)/(sqrt(1-x^(2)))), if x in(1/sqrt(2),1)

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate log{x+2+sqrt(x^2+4x+1)} with respect to x :

    Text Solution

    |

  2. Differentiate (sin^(-1)x^4)^4 with respect to x :

    Text Solution

    |

  3. Differentiate sin^(-1)(x/(sqrt(x^2+a^2))) with respect to x :

    Text Solution

    |

  4. Differentiate (e^xsinx)/((x^2+2)^3) with respect to x .

    Text Solution

    |

  5. Differentiate 3\ e^(-3x)log(1+x)

    Text Solution

    |

  6. Differentiate the following functions with respect to (x^2+2)/(sqrt...

    Text Solution

    |

  7. Differentiate (x^2(1-x^2)^3)/(cos2x) with respect to x .

    Text Solution

    |

  8. Differentiate log{cot(pi/4+x/2)} with respect to x :

    Text Solution

    |

  9. Differentiate the following functions with respect to e^(a x)secxta...

    Text Solution

    |

  10. Differentiate log(cosx^2) with respect to x :

    Text Solution

    |

  11. Differentiate cos(logx)^2 with respect to x :

    Text Solution

    |

  12. Differentiate logsqrt((x-1)/(x+1)) with respect to x :

    Text Solution

    |

  13. If y=log{sqrt(x-1)-sqrt(x+1)} , show that (dy)/(dx)=(-1)/(2sqrt(x^2-1)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. If y=log(sqrt(x)+1/(sqrt(x))) , prove that (dy)/(dx)=(x-1)/(2x(x+1))

    Text Solution

    |

  17. If y=logsqrt((1-tanx)/(1+tanx)) , prove that (dy)/(dx)=-sec2x .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove that (dy)/(dx)=1-y^2

    Text Solution

    |