Home
Class 12
MATHS
Suppose that f(0)=0a n df^(prime)(0)=2, ...

Suppose that `f(0)=0a n df^(prime)(0)=2,` and let `g(x)=f(-x+f(f(x)))dot` The value of `g'` (0) is equal to _____

Text Solution

Verified by Experts

`g(x)=f(-x+f(f(x))), f(0)=0, f'(0)=2`
`g'(x)=f'(-x+f(f(x)))cdot[-1+f'(f(x))cdotf'(x)]`
`g'(0)=f'(f(0))cdot[-1+f'(0)cdotf'(0)]`
`=f'(0)[-1+(2)(2)]=(2)(3)=6`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise JEE Previous Year|15 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answers Type|3 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Suppose that f(0)=0 and f'(0)=2, and let g(x)=f(-x+f(f(x))). The value of g'(0) is equal to -

Suppose that f(0)=0 and f'(0)=2, and let g(x)=f(-x+f(f(x))). The value of g (0) is equal to

If f(x)=sin x and g(x)=f(f(f,.....(f(x)))) then value of g'(0)+g''(0)+g'''(0) equals

If g(x)=(x^(2)+2x+3) f(x),f(0)=5 and lim_(x to 0) (f(x-5))/(x)=4 , then g'(0) is equal to

CENGAGE-DIFFERENTIATION-Exercise (Numerical)
  1. f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(p...

    Text Solution

    |

  2. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

    Text Solution

    |

  3. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) then c is equal to

    Text Solution

    |

  4. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

    Text Solution

    |

  5. Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value ...

    Text Solution

    |

  6. y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x)...

    Text Solution

    |

  7. If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime...

    Text Solution

    |

  8. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

    Text Solution

    |

  9. lim(hrarr0) ((e+h)^(In(e+h))-e)/(h) is-

    Text Solution

    |

  10. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

    Text Solution

    |

  11. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

    Text Solution

    |

  12. A nonzero polynomial with real coefficients has the property that f(x)...

    Text Solution

    |

  13. A function is reprersented parametrically by the equations x=(1+t)/(t^...

    Text Solution

    |

  14. Let z=(cosx)hat5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=...

    Text Solution

    |

  15. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

    Text Solution

    |

  16. Let f(x)=x+1/(2x+1/(2x+1/(2x+oo))) Compute the value of f(50)dotf^(p...

    Text Solution

    |

  17. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are...

    Text Solution

    |

  18. "If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)...

    Text Solution

    |

  19. Let y be an implicit function of x defined by x^(2x)-2x^xcot y-1=0....

    Text Solution

    |

  20. Let f:""(1,""1)vecR be a differentiable function with f(0)""=""1""a...

    Text Solution

    |