Home
Class 12
MATHS
Let F(x)=e^x,G(x)=e^(-x) " and " H(x)=G(...

Let `F(x)=e^x,G(x)=e^(-x) " and " H(x)=G(F(x))`, where x is a real variable. Then `(dH)/(dx)` at x=0 is

A

1

B

-1

C

`-1/e`

D

`-e`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|30 Videos
  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise HIGHER ORDER DERIVATIVES|32 Videos
  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos
  • INTEGRATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|29 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

Let f(x)=x, g(x)=1//x and h(x)=f(x) g(x). Then, h(x)=1, if

let f(x)=e^(x),g(x)=sin^(-1)x and h(x)=f(g(x)) th e n fin d (h'(x))/(h(x))

Let f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ,where [.] is the greatest integer function . Then h(-1) is

If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x) , then the value of g'(x) is

Let f(x)=e^(x)g(x),g(0)=4 and g'(0)=2, then f'(0) equals

Let f(x)=sinx,g(x)=x^(2) and h(x)=log_(e)x. If F(x)=("hog of ")(x)," then "F''(x) is equal to

TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. Find the differentiation of (e^(2x)+e^(-2x))/(e^(2x)-e^(-2x)) w.r.t. \...

    Text Solution

    |

  2. if y=logx*e^((tanx+x^(2))), then (dy)/(dx) is equal to

    Text Solution

    |

  3. Let F(x)=e^x,G(x)=e^(-x) " and " H(x)=G(F(x)), where x is a real varia...

    Text Solution

    |

  4. let f(x)=e^x ,g(x)=sin^(- 1) x and h(x)=f(g(x)) t h e n f i n d (h^(pr...

    Text Solution

    |

  5. If f(x)=(1)/(1-x), then the derivative of the composite function f[f{f...

    Text Solution

    |

  6. If y=f((2x-1)/(x^(2)+1)) and f^'(x)=sinx^(2), then (dy)/(dx) is equal ...

    Text Solution

    |

  7. If g(x) is the inverse function of f(x) and f'(x)=(1)/(1+x^(4)), then ...

    Text Solution

    |

  8. Let f : (-1,1) to R be a differentiabale function with f(0) = -1 and f...

    Text Solution

    |

  9. given y=(5x)/(3*sqrt(1-x)^2)+cos^2(2x+1),find dy/dx

    Text Solution

    |

  10. If y = f(x^(2) + 2) " and " f'(3) = 5 , " then" dy/dx " at x " = 1 is

    Text Solution

    |

  11. If f (x) = log(x) (log x), then f'(x) at x = e is …….. .

    Text Solution

    |

  12. If f(x)=sqrt(1+cos^2(x^2)),thenf'(sqrtpi/2) is

    Text Solution

    |

  13. If : f(x)=(sin^(2)x)/(1+cotx)+(cos^(2)x)/(1+tanx)," then: "f'((pi)/(4)...

    Text Solution

    |

  14. d/(dx)tan^-1((1-x)/(1+x))=

    Text Solution

    |

  15. If y =tan ^(-1) ((sqrt( a) -sqrt(x)) /( 1+sqrt( ax)) ) ,then (dy)/(dx)...

    Text Solution

    |

  16. If y=tan^(-1)[(sinx-cosx)/(cosx-sinx)] then (dy)/(dx) is

    Text Solution

    |

  17. If y= tan ^(-1) ((acos x -bsin x )/( bcos x+asin x ) ) ,then (dy)/(dx...

    Text Solution

    |

  18. यदि y= sec tan ^(-1) x, तब (dy)/(dx) =

    Text Solution

    |

  19. the derivative of tan^-1 (6xsqrtx)/(1-9x^3) is sqrtx g(x) then g(x) is...

    Text Solution

    |

  20. If y= e^(m sin ^(-1)) x and (1-x^(2))((dy)/(dx))^(2)= Ay^(2). then ...

    Text Solution

    |