Home
Class 12
MATHS
If y^x=e^(y-x), prove that (dy)/(dx)=((1...

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

Promotional Banner

Topper's Solved these Questions

  • CUET MOCK TEST 2022

    XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

If x^y= y^x , prove that (dy)/(dx)=((y/x-logy))/((x/y-logx))

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

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

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

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

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Consider f\ : R+vec[4,oo) given by f(x)=x^2+4 . Show that f is inve...

    Text Solution

    |

  2. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

    Text Solution

    |

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

    Text Solution

    |

  4. Write the cartesian equation of a plane, bisecting the line segment...

    Text Solution

    |

  5. Solve the following differential equation: y\ dx+xlog(y/x)dy=2x\ dy

    Text Solution

    |

  6. Find the particular solution of the following differential equation...

    Text Solution

    |

  7. Write the value of sin[pi/3-sin^(-1)(-1/2)]

    Text Solution

    |

  8. For a\ 2\ xx\ 2\ matrix, A=[a(i j)], whose elements are given by a...

    Text Solution

    |

  9. Evaluate: int1^3(2x^2+5x)dx as limit of a sum

    Text Solution

    |

  10. State the reason for the relation R in the set {1, 2, 3} given by R=...

    Text Solution

    |

  11. Write the value of intsecx\ (secx+tanx)\ dx

    Text Solution

    |

  12. Write the value of int(dx)/(x^2+16)

    Text Solution

    |

  13. For what value of x, the matrix [(5-x,x+1),(2,4)] is singular?

    Text Solution

    |

  14. Write A^-1 for A=[(2,5),(1,3)]

    Text Solution

    |

  15. For what value of a the vectors 2 hat i-\ 3 hat j+4 hat k and a h...

    Text Solution

    |

  16. Write the direction cosines of the vector -2 hat i+ hat j-5 hat k

    Text Solution

    |

  17. The length x of a rectangle is decreasing at the rate of 5 cm/minut...

    Text Solution

    |

  18. Find the intervals in which the function f given f(x)=\ sin x+cosx ,\...

    Text Solution

    |

  19. Write the principal value of tan^(-1)(1)+cos^(-1)(-1/2)

    Text Solution

    |

  20. Suppose a girl throws a dice. If she gets 5 or 6 she tosses a coin thr...

    Text Solution

    |