Home
Class 12
MATHS
If y=(e^x-e^(-x))/(e^x+e^(-1)),"p r o v ...

If `y=(e^x-e^(-x))/(e^x+e^(-1)),"p r o v et h a t"(dy)/(dx)=1-y^2`

A

`1 + y^(2)`

B

`1-y^(2)`

C

` y^(2)-1`

D

`y^(2)-2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Section -B|35 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Section - C ( More than one options are correct )|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Try youself|16 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

  • DETERMINANTS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

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

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

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

If x y^2=1,p rov et h a t2(dy)/(dx)+y^3=0

If y=(xsin^(-1)x)/(sqrt(1-x^2)),"p r o v et h a t"(1-x^2)(dy)/(dx)=x+y/xdot

If y=sqrt((1-x)/(1+x)),p rov et h a t(1-x^2)(dy)/(dx)+y=0

If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e)) , prove that (dy)/(dx)=e^(x^(e^x)) . x^(e^x){(e^x)/x+e^x.logx}+x^(e^(e^x)).e^(e^x){1/x+e^xdotlogx}+e^(x^(x^e)).x^(x^e).x^(e-1){1+elogx}

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

If y=x+1/(x+1/(1/(x+))), p rov et h a t(dy)/(dx)=y/(2y-x)

If x=(e^(t)+e^(-t))/(2),y=(e^(t)-e^(-t))/(2)," then: "(dy)/(dx)=

AAKASH INSTITUTE ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
  1. Differential coefficient of log10 x w.r.t logx 10 is

    Text Solution

    |

  2. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

    Text Solution

    |

  3. If y=(e^x-e^(-x))/(e^x+e^(-1)),"p r o v et h a t"(dy)/(dx)=1-y^2

    Text Solution

    |

  4. If y=ae^(mx)+be^(-mx) then (d^2y)/(dx^2) is

    Text Solution

    |

  5. If y^(2) = ax^(2) + b , " then " (d^(2)y)/( dx^(2))

    Text Solution

    |

  6. If y=(log x)/(x) then (d^(2)y)/(dx^(2))=

    Text Solution

    |

  7. Differentiate the following w.r.t.x. The differentiation coneffiecient...

    Text Solution

    |

  8. If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

    Text Solution

    |

  9. If f(x) = cos x cdot cos 2x cdot cos 4x cdot cos 8x cdot cos 16x," the...

    Text Solution

    |

  10. If y=cos^(-1)(cosx),then (dy)/(dx) at x=(5pi)/4 is equal to (a)1 (b)-...

    Text Solution

    |

  11. If x=e^(y+e^(y+e^(y+...oo))),xgt0, then (dy)/(dx) is equal to

    Text Solution

    |

  12. if x^y . y^x =16 then dy/dx at (2,2) is equal to

    Text Solution

    |

  13. If y = sin x^(@) " and " u = cos x " then " (dy)/(du) is equal to

    Text Solution

    |

  14. Let the function y = f(x) be given by x= t^(5) -5t^(3) -20t +7 ...

    Text Solution

    |

  15. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

    Text Solution

    |

  16. Find the derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2))...

    Text Solution

    |

  17. If t(1+x^(2))=x and x^(2)+t^(2)=y then at x = 2, the value of (dy)/(dx...

    Text Solution

    |

  18. If x=tcost ,y=t+sint . Then (d^2 x)/(dy^2)at t=pi/2 is (a)(pi+4)/2...

    Text Solution

    |

  19. if y = sin 2x , " then " (d^(6)y)/(dx^(6)) " at" x = pi/2 is equal t...

    Text Solution

    |

  20. Let f(x)=|[x^3,sinx,cosx],[6,-1, 0],[p, p^2,p^3]|, where p is a cons...

    Text Solution

    |