Home
Class 12
MATHS
If y=sqrt((1+e^x)/(1-e^x)),s howt h a t...

If `y=sqrt((1+e^x)/(1-e^x)),s howt h a t(dy)/(dx)=(e^x)/((1-e^x)sqrt(1-e^(2x)))`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

int(e^x)/((1+e^x)(2+e^x))dx

If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot

If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot

If e^x+e^y=e^(x+y),p rov e t h a t(dy)/(dx)+e^(y-x)=0

If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

If sqrt(y+x)+sqrt(y-x)=c ,s howt h a t(dy)/(dx)=y/x-sqrt((y^2)/(x^2)-1.)

If y=cos^(-1)sqrt((cos3x)/(cos^3x)),t h e ns howt h a t(dy)/(dx)=sqrt(3/(cosxcos3x))

If y=(sqrt(x))^sqrt(x)^sqrt(x)^(dot)^(((oo))),s howt h a t(dy)/(dx)=(y^2)/(x(2-ylogx)

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

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

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following functions with respect to x : sec(logx^n)...

    Text Solution

    |

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

    Text Solution

    |

  3. If y=sqrt((1+e^x)/(1-e^x)),s howt h a t(dy)/(dx)=(e^x)/((1-e^x)sqrt(1...

    Text Solution

    |

  4. Differentiate the following functions with respect to x : (log)(10...

    Text Solution

    |

  5. If =(sqrt(a^2+x^2)+sqrt(a^2-x^2))/(sqrt(a^2+x^2)-sqrt(a^2-x^2)) , show...

    Text Solution

    |

  6. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)x ,x...

    Text Solution

    |

  7. Differentiate tan^(-1)((1+2x)/(1-2x))w i t hr e s p e c ttosqrt(1+4x^2...

    Text Solution

    |

  8. Differentiate x^x with respect to xlogxdot

    Text Solution

    |

  9. Differentiate sin^(-1)((2x)/(1+2x)) wrt to tan^(-1)x , -1<x<1.

    Text Solution

    |

  10. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

    Text Solution

    |

  11. If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt(...

    Text Solution

    |

  12. Differentiate logsinx with respect to sqrt(cosx) .

    Text Solution

    |

  13. Find (dy)/(dx),w h e n x=e^(theta)(theta+1/theta)a n dy=e^(-theta)(th...

    Text Solution

    |

  14. If f(x)=|x+a^2a b a c a b x+b^2b c a bb c x+c^2|,fin df^(prime)(x)dot

    Text Solution

    |

  15. Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x...

    Text Solution

    |

  16. Differentiate the following functions with respect to x : (x^2+x+1)^...

    Text Solution

    |

  17. Differentiate the following functions with respect to x : (i)logsinx^...

    Text Solution

    |

  18. Differentiate log sinx from first principle.

    Text Solution

    |

  19. If f(x)=|logx|,xgt0,find f^(prime)(1/e)a n df^(prime)(e)

    Text Solution

    |

  20. Differentiate sin^(-1)sqrt(x)(0ltxlt1) from first principles.

    Text Solution

    |