d/(dx)cos^(-1)sqrt(cosx)i se q u a lto ...

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

A

`(1)/(2)sqrt(1+sec x)`

B

`sqrt(1+sec x)`

C

`-(1)/(2)sqrt(1+sec x)`

D

`-sqrt(1+sec x)`

Text Solution

Verified by Experts

`(d)/(dx)cos^(-1)sqrt(cos x)=(sin x)/(2sqrt(cos x)sqrt(1-cos x))`
`=(sqrt(1- cos^(2)x))/(2sqrt(cos x)sqrt(1-cos x))=(1)/(2)sqrt((1+cos x)/(cos x))`

Promotional Banner

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

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

Prove that I =int_(0)^(pi//2)(sqrt(secx))/(sqrt("cosec"x)+sqrt(secx))dx =pi/4

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

lim_(x->0)("cos"(tanx)-cosx)/(x^4)i se q u a lto 1/6 (b) -1/3 (c) 1/2 (d) 1

secx = - sqrt(2) .

Prove that tan^(-1) {(sqrt(1+cos x)+sqrt(1-cosx))/(sqrt(1+cos x)-sqrt(1-cosx))}=pi/4+x/2

y=tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) show that dy/dx=1/(2sqrt(1-x^2))

int(secx)/(sqrt(cos2x)) dx is equal to

intsqrt(e^x-1)dx is equal to (a) 2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c (b) sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)+c (c) sqrt(e^x-1)+tan^(-1)sqrt(e^x-1)+c (d) 2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c

CENGAGE PUBLICATION-DIFFERENTIATION-Execrises

If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...
Text Solution
|
If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (a) (sqrt...
Text Solution
|
d/(dx)cos^(-1)sqrt(cosx)i se q u a lto 1/2sqrt(1+s e cx) (b) sqrt(1+s...
Text Solution
|
If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx) at x=0 is
Text Solution
|
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
|
If y=(log)(sinx)(tanx),t h e n(((dy)/(dx)))(pi/4)i se q u a lto 4/(lo...
Text Solution
|
Evaluate,d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))] is
Text Solution
|
The differential coefficient of f(logex) with respect to x, where f(x)...
Text Solution
|
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
|
If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...
Text Solution
|
A function f, defined for all positive real numbers, satisfies the equ...
Text Solution
|
Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(...
Text Solution
|
The function f(x)=e^x+x , being differentiable and one-to-one, has a d...
Text Solution
|
If f(x) = x + tan x and f is the inverse of g, then g'(x) is equal to
Text Solution
|
If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the val...
Text Solution
|
If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)(dy)/(dx) is equal to (a)...
Text Solution
|
If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...
Text Solution
|
d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b...
Text Solution
|
Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...
Text Solution
|
answeer the following : (i) if y sqrt(x^2+1)=log(sqrt(x^2+1)-x), show ...
Text Solution
|