Home
Class 12
MATHS
If x^y = e^(x-y) " then " dy/dx ?...

If `x^y = e^(x-y) " then " dy/dx ?`

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|Exercise Exercies 5p|20 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.1|34 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5n|11 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If x^(y) = e^(2(x-y)), "then" (dy)/(dx) is equal to

If x^(2y)=e^(x-y)," then "(dy)/(dx)=

If x^(y)=e^(x-y) then (a) (dy)/(dx) doesn't exist at x=1 (b) (dy)/(dx)=0 when x=1 (c) (dy)/(dx)=(1)/(2) when x=e (d) none of these

If x^(y)=e^(x-y), then find (dy)/(dx)atx=1

If y = e^(x). cot x then (dy)/(dx) will be

If y=e^(x-y) then show that (dy)/(dx) = y/(1+y)

If tan(x+y)=e^(x+y) , then (dy)/(dx)

If x^(y)=e^(x-y), show that (dy)/(dx)=(y(x-y))/(x^(2))

If x^(y)=e^(x-y), show that (dy)/(dx)=(log x)/({log(xe)}^(2))

NAGEEN PRAKASHAN-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) = tan x is a continuous funct...

    Text Solution

    |

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

    Text Solution

    |

  4. the function f(x)={sinx/x+cosx , x!=0 and f(x)=k , x=0 is continuous a...

    Text Solution

    |

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

    Text Solution

    |

  6. The function f(x) = 2x - |x|

    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 " x dy/dx = ?

    Text Solution

    |

  13. If x^y = e^(x-y) " then " dy/dx ?

    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

    |