Home
Class 12
MATHS
Let f : (-5,5)rarrR be a differentiable ...

Let `f : (-5,5)rarrR` be a differentiable function of with `f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) = If g(x)=(f(2f^(2)(x)+2))^(2),` then g'(0) equals

A

4

B

-4

C

8

D

-8

Text Solution

Verified by Experts

`g'(x)=2f(2f^(2)(x)+2)xxf'(2f^(2)(x)+2)xx4f(x)cdotf'(x)`
`therefore" "g'(0)=2f(2f^(2)(0)+2)xxf'(2f^(2)(0)+2)xx4f(0)cdotf'(0)`
`=2f(4)cdotf'(4)cdot4f(0)f'(0)`
`=2xx4(-1)(1)`
`=-8`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Let f : (-1,1) to R be a differentiabale function with f(0) = -1 and f'(0) = 1. Let g(x) = [f(2f(x)+2)]^(2) , then g'(0)=

Let f:(-1,1)rarr R be a differentiable function with f(0)=-1 and f'(0)=1. Let g(x)=[f(2f(x)+2)]^(2)* Then g'(0)*-4(b)0(c)-2 (d) 4

Let f : (-1,1) to R be a differentiable function with f(0) =-1 and f'(0)=1 Let g(x)= [f(f(2x)+1)]^2 . Then g'(0)=

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

    Text Solution

    |

  2. A function f, defined for all positive real numbers, satisfies the equ...

    Text Solution

    |

  3. Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(...

    Text Solution

    |

  4. The function f(x)=e^(x)+x, being differentiable and one- to -one, has ...

    Text Solution

    |

  5. If f(x) = x + tan x and f is the inverse of g, then g'(x) is equal to

    Text Solution

    |

  6. If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the val...

    Text Solution

    |

  7. If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to x+y...

    Text Solution

    |

  8. " If "y=sqrt(logx+sqrt(logx+sqrt(logx+...oo)))," then "(dy)/(dx) is

    Text Solution

    |

  9. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=

    Text Solution

    |

  10. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  11. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

    Text Solution

    |

  12. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

    Text Solution

    |

  13. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

    Text Solution

    |

  14. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

    Text Solution

    |

  15. If y=(x^x)^x then (dy)/(dx) is

    Text Solution

    |

  16. The first derivative of the function [cos^(-1)(sin sqrt((1+x)/2))+x^x]...

    Text Solution

    |

  17. f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)'...

    Text Solution

    |

  18. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  19. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

    Text Solution

    |

  20. Suppose f(x)=e^(ax)+e^(bx)," where " a ne b, and that f''(x) -2f'(x)-1...

    Text Solution

    |