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

  • QUESTION PAPER 2017

    CHHAYA PUBLICATION|Exercise UNIT-4|4 Videos
  • QUESTION PAPER 2017

    CHHAYA PUBLICATION|Exercise UNIT-2|6 Videos
  • QUESTION PAPER -2018

    CHHAYA PUBLICATION|Exercise WBJEE|45 Videos
  • QUESTIONS PAPER -2019

    CHHAYA PUBLICATION|Exercise WBJEE 2019|45 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=(e^-x)/(1+[x]) , then

Let f(x)=a^(x)(a gt 0) be written as f(x)=g(x)+h(x) where g(x) is an even function and h(x) is an odd function. Then the value of g(x+y)+g(x-y) is -

If f(x)=e^xg(2x),g(0)=4 and g'(0) = 2 then f'(0) is equal to

Let f(x)=sinx,g(x)=x^2 and h(x) = log x. If F(x)=(h(f(g(x)))) , then F'(x) is:

f(x)=e^x.g(x) , g(0)=2 and g'(0)=1 then f'(0)=

Let F(x)=f(x)g(x)h(x) for all real x , where f(x),g(x) , and h(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0) . Then k is________

If f(x)=e^(x+a),g(x)=x^(b^2)and h(x)=e^(b^2x), find the value of (g[f(x)])/(h(x)).

If f(x) = e^(x + a) , g(x) = x^(b^2) and h(x) = e^(b^2 x) , then find the value of (g{f(x)})/(h(x))

If the function f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x) , then the value of g'(1) is

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

CHHAYA PUBLICATION-QUESTION PAPER 2017-UNIT-3
  1. Cosider the non-constant differentiable function f of one variable wh...

    Text Solution

    |

  2. If f(x)=log5log3 x, then f'(e ) 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. If f''(0)=k,kne0, then the value of lim(xto0)(2f(x)-3f(2x)+f(4x))/(x^...

    Text Solution

    |

  5. If y=e^(msin^-1x)(-1lexle1), Prove that, (1-x^2)(d^2y)/(dx^2)-xdy/dx...

    Text Solution

    |

  6. The chord of the curve y=x^2+2ax+b, joining the points where x=alpha "...

    Text Solution

    |

  7. Let f(x)={{:((x^p)/((sinx)q')),(0):}" if " 0ltxle(pi)/(2),(p,qinR) if ...

    Text Solution

    |

  8. lim(xto0)(sinx)^(2tanx)=

    Text Solution

    |

  9. intcos(logx)dx=F(x)+c, where c is an arbitaray constant. Here F(x)=

    Text Solution

    |

  10. Let I=int(10)^(19)(sinx)/(1+x^8)dx. Then,

    Text Solution

    |

  11. Let I1=int0^n[x]dx" and I2=int0^n{x}dx, where [x] and {x} are integral...

    Text Solution

    |

  12. Evalute : lim(ntooo)[(n)/(n^2+1^2)+(n)/(n^2+2^2)+........+(1)/(2n)].

    Text Solution

    |

  13. The value of the integral int0^1e^(x^2)dx

    Text Solution

    |

  14. int0^(100)e^(x-[x])dx=

    Text Solution

    |

  15. Solution of (x+y)^2(dy)/(dx)=a^2 ('a' being a constant ) is

    Text Solution

    |

  16. The integrating factor of the first order differential equation x^2(x^...

    Text Solution

    |

  17. If f(x)=int(-1)^x |t|dt, then for any xge0,f(x) is equal to

    Text Solution

    |

  18. Let for all xgt0,f(x)=lim(nto oo)n(x^((1)/(n))-1), then

    Text Solution

    |

  19. Let I=int0^(100pi)sqrt(1-cos2x)dx, then

    Text Solution

    |

  20. The area (sq. units) of the figure bounded by the parabolas x= -2y^2" ...

    Text Solution

    |