Home
Class 12
MATHS
find the derivative of e^(x) + e^(y) = ...

find the derivative of ` e^(x) + e^(y) = e^(x +y)`

A

` e^(x - y)`

B

`e^(x -y)`

C

`-e^(y-x)`

D

` e^(y-x)`

Text Solution

Verified by Experts

The correct Answer is:
C
` e^(x) + e^(y) = e ^(x+y) = e^(x) e^(y)`
` rArr e^(-y) + e^(-x) = 1`
On differentiating , both sides w.r.t.x, we get
`- e^(-y) (dy)/(dx) + e^(-x) (-1) = 0 `
` rArr (dy)/(Dx) = (e^(-x))/(-e^(-y))rArr (dy)/(dx) = -e^(y-x)` .
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|80 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

Similar Questions

Explore conceptually related problems

find the derivative of y=e^(x)log_(e)x

Find derivative of e^(x).tan x

Find nth derivative of x^(n)*e^(x)

Find the derivative of (e^(x))/(1 + x^(2))

Find derivative of y=e^(ax)sin bx

Find derivative of y=e^(ax)cos bx

find the derivative of y=e^(sin sqrt(x))

Find the derivative of y=(x^(3)+2^(x))/(e^(x))

Find the derivative of y=(e^(x))/(1+x^(2)) wrt x

Find first derivative of y w.r.t. x. (i) y=e^(-x) , (ii) y=4 sin 3x , (iii) y=4e^(x^(2)-2x)

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -MHT CET CORER
  1. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

    Text Solution

    |

  2. Find (dy)/(dx) , " if x " = 2 cos theta - cos 2 theta and y = 2sin...

    Text Solution

    |

  3. find the derivative of e^(x) + e^(y) = e^(x +y)

    Text Solution

    |

  4. If xy = tan^(-1) (xy) + cot^(-1) (xy), " then" (dy)/(dx) is equal to

    Text Solution

    |

  5. The derivative of cos^(3)x w.r.t. sin^(3)x is

    Text Solution

    |

  6. The derivative of log|x| is

    Text Solution

    |

  7. The function f(x)=e^(-|x|) is

    Text Solution

    |

  8. If f(x)=sin^(-1) ((2x)/(1+x^2)) then f(x) is differentiable on

    Text Solution

    |

  9. If y = log(cos x) sin x " then" (dy)/(dx) is equal to

    Text Solution

    |

  10. If y^(2) = ax^(2) + bx + c , where a,b,c, are constants , then y^...

    Text Solution

    |

  11. If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |

  12. If y = 5^(x) x^(5) , " then" (dy)/(dx) is

    Text Solution

    |

  13. If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy...

    Text Solution

    |

  14. (d)/(dx)[sec{cos^(-1) ((x)/(8))}] is equal to

    Text Solution

    |

  15. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is

    Text Solution

    |

  16. If y = a sin^(3) theta " and " x = a cos^(3) theta . " then at " th...

    Text Solution

    |

  17. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ . . .oo))), then (dy)/(dx) is equa...

    Text Solution

    |

  18. The nth derivatiive of (x+1)^n is

    Text Solution

    |

  19. If y = a sin (5x + c) , then

    Text Solution

    |

  20. If sin (xy) + (x)/(y) =x^(2) - y , " then " (dy)/(dx) is equal to

    Text Solution

    |