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

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

Text Solution

AI Generated Solution

To prove that \(\frac{dy}{dx} = \sqrt{y^2 - 4}\) for \(y = e^x + e^{-x}\), we will follow these steps: ### Step 1: Differentiate \(y\) Given: \[ y = e^x + e^{-x} \] We differentiate \(y\) with respect to \(x\): ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

If e^(x)+e^(y)=e^(x+y), prove that (dy)/(dx)=-(e^(x)(e^(y)-1))/(e^(y)(e^(x)-1)) or,(dy)/(dx)+e^(y-x)=0

If e^(x)+e^(y)=e^(x+y), prove that (dy)/(dx)+e^(y-x)=0

If e^(x)+e^(y)=e^(x+y), prove that (dy)/(dx)+e^(y-x)=0

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

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

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=x\ sin^(-1)x+sqrt(1-x^2) , prove that (dy)/(dx)=sin^(-1)x

    Text Solution

    |

  2. If y=sqrt(x^2+a^2) , prove that y(dy)/(dx)-x=0

    Text Solution

    |

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

    Text Solution

    |

  4. If y=sqrt(a^2-x^2) , prove that y(dy)/(dx)+x=0

    Text Solution

    |

  5. If x y=4 , prove that x((dy)/(dx)+y^2)=3y

    Text Solution

    |

  6. Prove that d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)x/a}=sqrt(a^2-x^2)

    Text Solution

    |

  7. Differentiate sin^(-1)(sinx),\ \ x in [0,\ 2pi]

    Text Solution

    |

  8. Differentiate cos^(-1)(cosx),\ \ x in [0,\ 2pi]

    Text Solution

    |

  9. Differentiate tan^(-1)(tanx),\ \ x in [0,\ pi]-{pi/2}

    Text Solution

    |

  10. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x , if -1/(sqrt(...

    Text Solution

    |

  11. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x , if 1/(sqrt(2...

    Text Solution

    |

  12. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x theta in [-(pi...

    Text Solution

    |

  13. Differentiate sin^(-1)(3x-4x^3) with respect to x , if -1/2ltxlt1/2

    Text Solution

    |

  14. Differentiate sin^(-1)(3x-4x^3) with respect to x , if 1/2ltxlt1

    Text Solution

    |

  15. Differentiate sin^(-1)(3x-4x^3) with respect to x , if -1ltxlt-1/2

    Text Solution

    |

  16. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0ltxlt1

    Text Solution

    |

  17. Differentiate cos^(-1)(2x^2-1) with respect to x , if -1ltxlt0

    Text Solution

    |

  18. Differentiate cos^(-1)(1-2x^2) with respect to x , if 0ltxlt1

    Text Solution

    |

  19. Differentiate cos^(-1)(1-2x^2) with respect to x , if -1ltxlt0

    Text Solution

    |

  20. Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (-1/2,1/2)

    Text Solution

    |