Home
Class 12
MATHS
If x^y = e^(x + y) , show that (dy)/(dx)...

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

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION XII)(SHORT ANSWER TYPE QUESTIONS) |12 Videos

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )|45 Videos

Similar Questions

Explore conceptually related problems

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

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

Differentiate the following w.r.t.x. If y^x = e^(y - x) , prove that (dy)/(dx) = ((1 + log y)^2)/(log y)

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

Differentiate the following w.r.t.x. If x^y = y^x , prove that (dy)/(dx) = (y/x - "log y")/(x/y- "log x")

Differentiate the following w.r.t.x. y = x^(x^(x^( oo))) , prove that x (dy)/(dx) = (y^2)/(1 - y log x)

If y = e^(x + 3 log x) prove that dy/dx = x^2 (x+3) e^x

BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. Find all the points of discontinuity of f, where f is defined by f(x...

    Text Solution

    |

  2. Find (dy)/(dx) if y = log (sqrt(2x + sqrt(4x^2 + a^2)))

    Text Solution

    |

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

    Text Solution

    |

  4. If siny = xsin(a+y), prove that dy/dx=sin^2(a+y)/sina

    Text Solution

    |

  5. Differentiate cos^(-1) ((1 - x^2)/(1 + x^2)) , 0 lt x lt 1. w.r.t.x

    Text Solution

    |

  6. Diferentiate tan^(-1)((2x)/(1 - x^2)) w.r.t.x.

    Text Solution

    |

  7. If y = a sin (log x) + b cos (log x), then prove that : x^2 d^2y/dx^2+...

    Text Solution

    |

  8. If y=sin(msin^-1x), prove that (1-x^2)y2-xy1+m^2y=0

    Text Solution

    |

  9. Discuss the continuity of f(x) = 0 at x = 0 if f(x) = {{:((sqrt(1 + ...

    Text Solution

    |

  10. Discuss the continuity of following at x = 0 if f(x) = {{:((sqrt(1 +...

    Text Solution

    |

  11. Determine the value of constant k so that the function f(x) = {{:((x...

    Text Solution

    |

  12. Determine the constant k, so that the function f(x) = {{:((x^2- 9)/(...

    Text Solution

    |

  13. Examine the continuity of the following function at x = 2 : f(x) = {...

    Text Solution

    |

  14. Examine the continuity of the following function at x = 2 : f(x) = {...

    Text Solution

    |

  15. Differentiate the following w.r.t.x y = log(x+4+sqrt(x^2 +8x+4))

    Text Solution

    |

  16. Differentiate the following w.r.t.x y= log(x+2+sqrt(x^2 + 4x+1))

    Text Solution

    |

  17. y = sqrt(cos x + sqrt(cosx + sqrt(cosx + ...."to " oo))) prove that (2...

    Text Solution

    |

  18. y = sqrt(sin x + sqrt(sinx + sqrt(sinx + ....1 oo))) prove that (2y - ...

    Text Solution

    |

  19. y = sqrt(tan x + sqrt(tanx + sqrt(tanx + ...."to" oo))) prove that (2y...

    Text Solution

    |

  20. If sin y = x cos (a + y), prove that (dy)/(dx) = (cos^2 (a + y))/(cos ...

    Text Solution

    |