Home
Class 12
MATHS
The derivative of y=(1-x)(2-x)....(n-x) ...

The derivative of `y=(1-x)(2-x)....(n-x) ` at ` x=1` is
(a)`0` (b) `(-1)(n-1)!` (c)`n !-1` (d) `(-1)^(n-1)(n-1)!`

A

0

B

`(-1) (n-1)!`

C

`n!-1`

D

`(-1)^(n-1)(n-1)!`

Text Solution

Verified by Experts

`(dy)/(dx)=-[(2-x)(3-x)...(n-x)+(1-x)(3-x)...(n-x)+...(1-x)(2-x)...(n-1-x)]`
At x = 1,
`(dy)/(dx)=-[(n-1)!+0+...+0]=(-1)(n-1)!`
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

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

The n t h derivative of x e^x vanishes when (a) x=0 (b) x=-1 (c) x=-n (d) x=n

(d^n)/(dx^n)(logx)=? (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

(x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

Find the coefficient of x^(-5) in ""^(n)C_(0)-""^(n)C_(1) ((2x-1)/(x))+""^(n)C_(2)((2x-1)/(x))^(2)-....+ (-1)^(n) ((2x-1)/(x))^(n)

The value of the determinant of n^(t h) order, being given by |[x, 1, 1...], [1, x, 1...], [1, 1, x...],[... , ... , ...]| is a. (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-1) d. none of these

The n t h derivative of the function f(x)=1/(1-x^2)[w h e r ex in (-1,1)] at the point x=0 where n is even is (a) 0 (b) n ! (c) n^n C_2 (d) 2^n C_2

If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is equal to (a) y (b) y+(x^n)/(n !) (c) y-(x^n)/(n !) (d) y-1-(x^n)/(n !)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n) "show that ", (1)/(1!(n-1)!)+(1)/(3!(n-3)!)+(1)/(5!(n-5)!)+....=(2^(n-1))/(n!)

If the straight line (x)/(h)+(y)/(k)=1 touches the curve (x/a)^(n)+((y)/(b))^(n)=1 , then show that ((a)/(h))^((n)/(n-1))+((b)/(k))^((n)/(n-1))=1

CENGAGE PUBLICATION-DIFFERENTIATION-Execrises
  1. If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]...

    Text Solution

    |

  2. If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/a ,t h e n(dy)/(dx) wherever it...

    Text Solution

    |

  3. The derivative of y=(1-x)(2-x)....(n-x) at x=1 is (a)0 (b) (-1)(n...

    Text Solution

    |

  4. " If "y=sqrt((1-x)/(1+x))," then "(1-x^(2))(dy)/(dx) is equal to

    Text Solution

    |

  5. If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se...

    Text Solution

    |

  6. Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=...

    Text Solution

    |

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

    Text Solution

    |

  8. Let h(x) be differentiable for all x and let f(x)=(k x+e^x)h(x) , wher...

    Text Solution

    |

  9. If lim(trarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2...

    Text Solution

    |

  10. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

    Text Solution

    |

  11. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (a) (sqrt...

    Text Solution

    |

  12. d/(dx)cos^(-1)sqrt(cosx)i se q u a lto 1/2sqrt(1+s e cx) (b) sqrt(1+s...

    Text Solution

    |

  13. if y = tan^-1(2^x/(1+2^(2x+1))) then dy/dx at x =0 is

    Text Solution

    |

  14. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (n y)/(sqrt(x^2+a^2)) (b...

    Text Solution

    |

  15. If y=e^ log(x^ 5 ) , find dy/ dx ​

    Text Solution

    |

  16. Evaluate,d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))] is

    Text Solution

    |

  17. The differential coefficient of f((log)e x) with respect to x , where ...

    Text Solution

    |

  18. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is ...

    Text Solution

    |

  19. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

    Text Solution

    |

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

    Text Solution

    |