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

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

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

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

Solve : (dy)/(dx)=e^(y-x)+2

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

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

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

If y= 3e^(2x)+2e^(3x) , prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=0 .

(dy)/(dx)=e^(x-y)+1

(dy)/(dx)+1=e^(x-y)

If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If y=e^(7x) +e^(-7x) , show that (d^(2)y)/(dx^(2))= 49y .

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. If ysqrt(1-x^2)+xsqrt(1-y^2)=1 when |x|lt1 and |y|lt1 find dy/dx

    Text Solution

    |

  2. If xsqrt(1+y)+ysqrt(1+x)=0, prove that dy/dx=(-1)/((1+x)^2

    Text Solution

    |

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

    Text Solution

    |

  4. Differentiate x^(sin^(-1)x) w.r.t 'x'

    Text Solution

    |

  5. If y= (x)^cosx,find dy/dx

    Text Solution

    |

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

    Text Solution

    |

  7. If y=e^(x+e^(x+e^(x+....TOoo))) prove that dy/dx=y/((1-y))

    Text Solution

    |

  8. Differentiate tan ^(-1)((sqrt(1+x^2 )-1)/x) w,r,t. tan ^(-1)x

    Text Solution

    |

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

    Text Solution

    |

  10. If y=sin^(-1) x, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0

    Text Solution

    |

  11. If x=a(theta+sin theta) and y=a(1-costheta), find (d^2y)/(dx^2)"at"the...

    Text Solution

    |

  12. A particle moves along the curve y=2/3x^3. Find the points on the curv...

    Text Solution

    |

  13. A man of height 1.6m, walks at a rate of 30m/sec away from a lamp whic...

    Text Solution

    |

  14. Water is leaking from a conical funnel at the rate of 5cm^3//sec. If t...

    Text Solution

    |

  15. Find the approximate value of log(10)10.1 it being given that log10e=0...

    Text Solution

    |

  16. The time T of of oscillation of a simple pendulum of length l is given...

    Text Solution

    |

  17. If in a triangle ABC, the side c and the angle C remain constant while...

    Text Solution

    |

  18. Find the interval in which f(x)=2x^3+3x^2-12x+1 is increasing.

    Text Solution

    |

  19. Find the interval in which f(x)=x^3-3x^2-9x+30 is strictly increasing ...

    Text Solution

    |

  20. The function f(x)=sin^4x+cos^4x increasing if :

    Text Solution

    |