Home
Class 12
MATHS
If f(x)=x^4tan(x^3)-x1n(1+x^2), then the...

If `f(x)=x^4tan(x^3)-x1n(1+x^2),` then the value of `(d^4(f(x)))/(dx^4)` at `x=0` is 0 (b) 6 (c) 12 (d) 24

Text Solution

Verified by Experts

`"As "f(x) = x^(4) tan (x^(3))-x" In "(1+x^(2))" is odd, "(d^(3)f(x))/(dx^(3))` is even
`"Hence, "(d^(4)f(x))/(dx^(4))=0at x = 0.`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|29 Videos
  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|23 Videos
  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.9|14 Videos
  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos
  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If f(x)= 4^x/(4^x-2) then find the value f(x)+f(1-x).

The maximum value of f(x)=x/(1+4x+x^2) is -1/4 (b) -1/3 (c) 1/6 (d) 1/6

If f (x) = tan ^(-1) ((cos x- sinx)/(cos x+ sin x)) then the value of (d)/(dx) f(x) is-

L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int_(1/4)^(3/4)f(f(x))dx)^(-1) is____

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is (a) a=10 : b=6 (b) a=4 : b=12 (c) a=12 : b=4 (d) a=6 : b=10

"If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+f''(2)+f'(3)+f'(4) equals

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

Let f(x) be positive, continuous, and differentiable on the interval (a , b)a n d lim_(x->a^+)f(x)=1,lim_(x->b^-)f(x)=3^(1/4)dot If f^(prime)(x)geqf^3(x)+1/(f(x)), then the greatest value of b-a is (a) pi/(48) (b) pi/(36) (c) pi/(24) (d) pi/(12)

If f(x)= {((tan 3x)/(4x),xne0 ),(k, x=0):} , then for what value of K, f(x) is continuous.

If f(x) = x+ 1/x , x>0 then the greatest value of f(x) is (a) -2 (b)0 (c) 3 (d) none of these

CENGAGE PUBLICATION-DIFFERENTIATION-Execrises
  1. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

    Text Solution

    |

  2. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

    Text Solution

    |

  3. If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is

    Text Solution

    |

  4. A function f satisfies the condition f(x)=f^(prime)(x)+f''(x)+f'''(x)....

    Text Solution

    |

  5. Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,...

    Text Solution

    |

  6. "If "y^(2)=ax^(2)+bx+c," then "y^(3)(d^(2)y)/(dx^(2)) is

    Text Solution

    |

  7. "If "y= cos x +e^(4x)," then "(d^(2)y)/(dx^(2))=

    Text Solution

    |

  8. If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and ...

    Text Solution

    |

  9. Let y=ln(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

    Text Solution

    |

  10. If x=tcost ,y=t+sint . Then (d^2 x)/(dy^2)at t=pi/2 is (a)(pi+4)/2...

    Text Solution

    |

  11. "Let "y=t^(12)+1 and x=t^(6)+1." Then "(d^(2)y)/(dx^(2)) is

    Text Solution

    |

  12. If x = log p and y=(1)/(p), then

    Text Solution

    |

  13. If x=varphi(t), y=psi(t),t h e n(d^2 y)/(dx^2) is (a)(varphi^(prime)ps...

    Text Solution

    |

  14. If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) ...

    Text Solution

    |

  15. Let g(x) be the inverse of an invertible function f(x), which is diffe...

    Text Solution

    |

  16. f(x)=e^(x)-e^(-x)-2 sin x -(2)/(3)x^(3). Then the least value of n for...

    Text Solution

    |

  17. Let y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda(z^(3))(dy)/(dz)...

    Text Solution

    |

  18. Let x=f(t) and y=g(t), where x and y are twice differentiable function...

    Text Solution

    |

  19. If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in ...

    Text Solution

    |

  20. A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+...

    Text Solution

    |