Home
Class 12
MATHS
If x^y=e^(x-y) , then (dy)/(dx) is (1+x)...

If `x^y=e^(x-y)` , then `(dy)/(dx)` is `(1+x)/(1+logx)` (b) `(1-logx)/(1+logx)` (c) not defined (d) `(logx)/((1+logx)^2)`

A

`1/log x `

B

`(1)/(log ex )^2`

C

`(log x )/(log ex )^2`

D

`1/(log ex )^2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5p|20 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.1|34 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5n|10 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If x^y=e^(x-y) , then (dy)/(dx) is (a) (1+x)/(1+logx) (b) (1-logx)/(1+logx) (c) not defined (d) (logx)/((1+logx)^2)

int(logx/(1+logx)^2)dx

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

If x^y=e^(x-y), Prove that (dy)/(dx)=(logx)/((1+logx)^2)

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

Find int[log(logx)+1/((logx)^2)]dx

Find int[log(logx)+1/((logx)^2)]dx

Evaluate: int(logx)/((1+logx)^2)dx

If y=x^((logx)^log(logx)) then (dy)/(dx)=

Evaluate int(logx)/((1+logx)^(2))dx .

NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Exercies 5o
  1. Discuss the continuity of the function f(x)={((|x|)/x", " xne 0)...

    Text Solution

    |

  2. Prove that the function defined by f(x) = t a n xis a continuous func...

    Text Solution

    |

  3. The function f(x)= {(2 ax ", " x le 3 ),( 3x +1 ", " x gt 3):}...

    Text Solution

    |

  4. The function f(x)={sinx/x +cosx , x!=0 and f(x) =k at x=0 is continuo...

    Text Solution

    |

  5. The function f(x)= {(5x-4 ", " 0 lt x le 1 ),( 4x^3-3x", " 1 l...

    Text Solution

    |

  6. Show that the function f(x)=2x-|x| is continuous at x=0 .

    Text Solution

    |

  7. The value of 'k' for which f(x)= {(kx^2", " x ge 2 ),(12", ...

    Text Solution

    |

  8. The value of k for which f(x)= {((1-cos 2x )/(x^2 )", " x ne 0 ),(...

    Text Solution

    |

  9. If the function f(x)= {(3ax +b", " x gt 1 ),(11 ", "x=...

    Text Solution

    |

  10. The value of 'a' for which f(x)= {((sin^2 ax)/(x^2)", " x ne 0 ),(...

    Text Solution

    |

  11. If y= sin ^-1\ (1)/(sqrt(1+x^2)) then dy/dx at x =0 is :

    Text Solution

    |

  12. If y=(x)/(x+5), then prove that x (dy)/(dx) = y(1 - y)

    Text Solution

    |

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

    Text Solution

    |

  14. If y= tan ^-1 ((x)/sqrt(a^2-x^2)) then dy/dx =?

    Text Solution

    |

  15. If y= tan^-1((1-x)/(1+x))+cot^-1((1-x)/(1+x)) then dy/dx= ?

    Text Solution

    |

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

    Text Solution

    |

  17. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...

    Text Solution

    |

  18. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to tan^(-1)((2...

    Text Solution

    |

  19. If f(x)= x^2+7x+10 then f'(2) =?

    Text Solution

    |

  20. At which point the slope to tangent is zero for the curvey y=x^2-6x+8 ...

    Text Solution

    |