(d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) ...

`(d^n)/(dx^n)(logx)=` `((n-1)!)/(x^n)` (b) `(n !)/(x^n)` `((n-2)!)/(x^n)` (d) `(-1)^(n-1)((n-1)!)/(x^n)`

A

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

B

`(n!)/(x^(n))`

C

`((n-2)!)/(x^(n))`

D

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

Text Solution

Verified by Experts

Let y=log x. `"Then,"`
`y_(1)=(1)/(x),y_(2)=(-1)/(x^(2)),y_(3)=(2)/(x^(3)),...,y_(n)=((-1)^(n-1)(n-1)!)/(x^(n)).`

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

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

(b) int(x^(n-1)dx)/(sqrt(a^n+x^n))

int(dx)/(x^(n)(1+x^(n))^((1)/(n)))

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

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^(+)(x+2)^(n-3)(x+1)^(2)++(x+1)^(n)(x+2)^(n-2)-(x+1)^(n) b.(x+2)^(n-2)-(x+1)^(n-1) c.(x+2)^(n)-(x+1)^(n) d.none of these

16.Prove that (x^(n))/(n)!+(x^(n-1)*a)/((n-1)!1!)+(x^(n-2)*a^(2))/((n-2)!2!)......+(a^(n))/(n!)=((x+a)^(n))/(n!)

If tan x=n tan y,n in R^(+), then the maximum value of sec^(2)(x-y) is equal to (a) ((n+1)^(2))/(2n) (b) ((n+1)^(2))/(n)( c) ((n+1)^(2))/(2) (d) ((n+1)^(2))/(4n)

if int(dx)/(x^(2)(x^(n)+1)^(((n-1)/(n))))=-[f(x)]^((1)/(n))+c,thenf(x)is(a)(1+x^(n))(b)1+x^(-1)(c)x^(n)+x^(-n)(d) none of these

If int(dx)/(x^(2)(x^(n)+1)^((n-1)/(n)))=-(f(x))^((1)/(n))+C then f(x) is (A)1+x^(n)(B)1+x^(-n)(C)x^(n)+x^(-n)(D)x^(n)-x^(-n)

CENGAGE-DIFFERENTIATION-Exercise (Single)

Suppose f(x)=e^(ax) + e^(bx), where a!=b, and that fprimeprime(x)-2fpr...
Text Solution
|
(d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto 2^(20)(cos2x-2^(20)os3x...
Text Solution
|
(d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d...
Text Solution
|
The n t h derivative of the function f(x)=1/(1-x^2)[w h e r ex in (-1,...
Text Solution
|
If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...
Text Solution
|
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
|
"If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...
Text Solution
|
If (sinx)(cosy)=1/2,t h e n(d^2y)/(dx^2)a t(pi/4,pi/4) is -4 (b) -2 (c...
Text Solution
|
A function f satisfies the condition f(x)=f^(prime)(x)+f^(x)+f^(x) ,w ...
Text Solution
|
Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,...
Text Solution
|
If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...
Text Solution
|
If y=sinx+e^x ,t h e n(d^(2x))/(dy^2)= (-sinx+e^x)^(-1) (sinx-e^x)/(...
Text Solution
|
If y= sin px and y(n) is the n^(th) derivative of y, then |{:(y,y(1)...
Text Solution
|
If f^(x)=-f(x)a n dg(x)=f^(prime)(x)a n d F(x)=(f(x/2))^2+(g(x/2))^2 ...
Text Solution
|
Let y=1n(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...
Text Solution
|
x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)a tt=pi/2 is (pi+4)/2 (b) -(p...
Text Solution
|
"If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+...
Text Solution
|
let y=t^(10)+1, and x=t^8+1, then (d^2y)/(dx^2) is
Text Solution
|
If x = log p and y=(1)/(p), then
Text Solution
|
If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^...
Text Solution
|