Home
Class 12
MATHS
If y=log(3x),\ \ x!=0 , find (dy)/(dx) ....

If `y=log(3x),\ \ x!=0` , find `(dy)/(dx)` .

Text Solution

Verified by Experts

`y = log |3x|`
`frac{dy}{dx}=(1)/(3x) .3`
`=1/x, x!=0`
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

y=log(3x^(2)+2x+1), find (dy)/(dx)

If y=log_(3)log_(3)x, find (dy)/(dx)

If y=log tan.(x)/(2) , find (dy)/(dx) .

If y=e^(x) log (sin 2x), find (dy)/(dx) .

If y=log x^(x)+x^( log x ), find dy/dx .

y=sin^(2)(log(2x+3)), find (dy)/(dx)

If 4x+3y=log(4x-3y), find (dy)/(dx)

If y=e^([log (x+1)-log x])." Find" (dy)/(dx)

If y=log x , find dy/dx

If x=te^(t) and y=1+log t, find (dy)/(dx)

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If u=sin^(-1)((2x)/(1+x^2)) and v=tan^(-1)((2x)/(1-x^2)) , where -1 < ...

    Text Solution

    |

  2. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

    Text Solution

    |

  3. If y=log(3x),\ \ x!=0 , find (dy)/(dx) .

    Text Solution

    |

  4. If f(x) is an even function, then write whether f^(prime)(x) is eve...

    Text Solution

    |

  5. If f(x) is an odd function, then write whether f^(prime)(x) is even...

    Text Solution

    |

  6. Write the derivative of sinx with respect to cosx .

    Text Solution

    |

  7. If f(x)=(log)(x^2)(logx) , then f^(prime)(x) at x=e is (a) 0 (b) 1 (c)...

    Text Solution

    |

  8. The differential coefficient of f(logx) with respect to x , where f(...

    Text Solution

    |

  9. The derivative of the function cot^(-1){(cos2x)^(1//2)} at x=pi//6 i...

    Text Solution

    |

  10. Differential coefficient of sec(tan^(-1)x) is (a)x/(1+x^2) (b) xsqrt...

    Text Solution

    |

  11. If y= tan^(-1)sqrt((1-sinx)/(1+sinx)), then the value of (dy)/(dx) at ...

    Text Solution

    |

  12. If y=(1+1/x)^x , then (dy)/(dx)= (a)(1+1/x)^x{log(1+1/x)-1/(x+1)} (b)...

    Text Solution

    |

  13. If x^y=e^(x-y) , then (dy)/(dx) is (a)(1+x)/(1+logx) (b) (1-logx)/(1+l...

    Text Solution

    |

  14. Given f(x)=4x^8 , then (a)f'(1/2)=f'(-1/2) (b) f(1/2)=-f'(-1/2) (c) f...

    Text Solution

    |

  15. If x=a\ cos^3theta,\ \ y=a\ sin^3theta , then (1+((dy)/(dx))^2)= (a)t...

    Text Solution

    |

  16. If y=sin^(-1)((1-x^2)/(1+x^2)) , then (dy)/(dx)= (a)-2/(1+x^2) (b) 2/...

    Text Solution

    |

  17. The derivative of sec^(-1)(1/(2x^2-1)) with respect to sqrt(1+3x) at x...

    Text Solution

    |

  18. For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is (a)1//...

    Text Solution

    |

  19. If sin(x+y)=log(x+y) , then (dy)/(dx)= (a) 2 (b) -2 (c) 1 (d) -1]

    Text Solution

    |

  20. Let U=sin^(-1)((2x)/(1+x^2)) and V=tan^(-1)((2x)/(1-x^2)) , then (d U)...

    Text Solution

    |