Home
Class 12
MATHS
Differentiate cos(logx)^2 with respect t...

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

Text Solution

Verified by Experts

Let `y=cos(logx)^2`
so,
`(dy)/(dx)=d/(dx)cos(logx)^2`
`=(-sin(logx)^2) d/(dx) (logx)^2`
`=(-2 log x sin(logx)^2)/x`
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 (cos x)^(x) with respect to x:

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

Differentiate sin(cos(x^(2))) with respect to x

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

Differentiate (x cos x)^(x) with respect to x

Differentiate (1+cos x)^(x) with respect to x:

Differentiate x cos^(-1)x with respect to x:

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

Differentiate (log x)^(cos x) with respect to x.

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

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate the following functions with respect to e^(a x)secxta...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If y=e^xcosx , prove that (dy)/(dx)=sqrt(2)\ e^xcos(x+pi/4)

    Text Solution

    |

  15. If y=1/2log((1-cos2x)/(1+cos2x)) , prove that (dy)/(dx)=2\ cos e c\ 2x

    Text Solution

    |

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

    Text Solution

    |

  17. If y=sqrt(x^2+a^2) , prove that y(dy)/(dx)-x=0

    Text Solution

    |

  18. If y=e^x+e^(-x) , prove that (dy)/(dx)=sqrt(y^2-4)

    Text Solution

    |

  19. If y=sqrt(a^2-x^2) , prove that y(dy)/(dx)+x=0

    Text Solution

    |

  20. If x y=4 , prove that x((dy)/(dx)+y^2)=3y

    Text Solution

    |