Home
Class 12
MATHS
If y = (e^x - e^-x)/(e^x + e^-x). Prove ...

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

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|788 Videos

  • APPLICATIONS OF INTEGRALS

    PRADEEP PUBLICATION|Exercise EXERCISE|162 Videos

  • DETERMINANTS

    PRADEEP PUBLICATION|Exercise EXERCISE|342 Videos

Similar Questions

Explore conceptually related problems

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

If y = (e^x - e^-x)/(e^x + e^-x) , then dy/dx =

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

If y = tan^-1((e^(2x) +1)/(e^(2x) -1)) , prove that : dy/dx =-(2e^(2x))/(1+e^4x)

Differentiate the following w.r.t.x. y = e^(x^(+ex + ex^(-"to" oo))), prove that (dy)/(dx) = y/(1 - y)

If y = e^(x + 3 log x) prove that dy/dx = x^2 (x+3) e^x

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

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

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

If y = sqrt((1+e^x)/(1-e^x)), show that dy/dx = e^x/((1-e^x) sqrt(1-e^2x)), x < 0

PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If y = (e^x - e^-x)/(e^x + e^-x). Prove that dy/dx = 1 - y^2

    Text Solution

    |

  2. Examine the continuity of f(x) = {:{((x^2-9)/(x-3), x ne 3),(6,x=3):} ...

    Text Solution

    |

  3. If f(X) = (x^2-1)/(x-1 for x ne 1 and f(x) = 2 when x = 1. Show that ...

    Text Solution

    |

  4. The value of the constant k so that the function f(x)={((x^(2)-3x+2)/...

    Text Solution

    |

  5. The constant k, so that the f(x) = {{:((x^(2) - 2x - 3)/(x + 1),"if",x...

    Text Solution

    |

  6. Examine the function f(X) = {:{((1-cos3x)/(x), x ne 0),(0,x=0):} for c...

    Text Solution

    |

  7. For what value of k, function f (x) is continuous at x = 0 where f(x) ...

    Text Solution

    |

  8. A function f(x) is defined as f(x) = {:{((x^2-x-6)/(x-3), x ne 3),(5,x...

    Text Solution

    |

  9. Discuss the continuity of the function f(x), where f(x)= {:{(2-x, x < ...

    Text Solution

    |

  10. Discuss the continuity of the function f(x) at x = 0 , where f(x) ={:{...

    Text Solution

    |

  11. Discuss the continuity of the function f(x) at x = 2, where f(x) = {:{...

    Text Solution

    |

  12. Discuss continuity of f(X) = {:{(-1,x<0),(2-x,xge0):} at x = 0

    Text Solution

    |

  13. Examine the following functions for continuity: f(x) = {:{((2x^2-3x-...

    Text Solution

    |

  14. Examine the following functions for continuity: f(x) = {:{(x+a,x<1),...

    Text Solution

    |

  15. Examine the following functions for continuity: f(x) = {:{((|x-3|)/(...

    Text Solution

    |

  16. Examine the following functions for continuity: f(x) = {:{((x-|x|)/x...

    Text Solution

    |

  17. Examine the following functions for continuity: f(x) = {:{((x^2/2), ...

    Text Solution

    |

  18. Examine the following functions for continuity: f(x) = |x| + |x-1| ...

    Text Solution

    |

  19. Examine the continuity of the function f(x) = {:{(3x-2,xle0),(x+1,x>0)...

    Text Solution

    |

  20. Is the function f(X) = {:{((1-x^n)/(1-x), x ne 1),(n-1,x=1):}, n in N ...

    Text Solution

    |

  21. If f(x) = {{:((x)/(|x| + 2x^2)"," ,x != 0),(k",", x = 0):} Prove tha...

    Text Solution

    |