मराठी

Differential coefficient of sec (tan–1x) w.r.t. x is ______.

Advertisements
Advertisements

प्रश्न

Differential coefficient of sec (tan–1x) w.r.t. x is ______.

पर्याय

  • `x/sqrt(1 + x^2)`

  • `x/(1 + x^2)`

  • `xsqrt(1 + x^2)`

  • `1/sqrt(1 + x^2)`

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

Differential coefficient of sec (tan–1x) w.r.t. x is `x/sqrt(1 + x^2)`.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Continuity And Differentiability - Solved Examples [पृष्ठ १०५]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 5 Continuity And Differentiability
Solved Examples | Q 32 | पृष्ठ १०५

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Differentiate the function with respect to x.

sin (x2 + 5)


Differentiate the function with respect to x.

sin (ax + b)


Differentiate the function with respect to x.

`sec(tan (sqrtx))`


Differentiate the function with respect to x.

`(sin (ax + b))/cos (cx + d)`


Differentiate the function with respect to x. 

cos x3 . sin2 (x5)


Differentiate the function with respect to x:

`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`


If f(x) = |x|3, show that f"(x) exists for all real x and find it.


If y = `[(f(x), g(x), h(x)),(l, m,n),(a,b,c)]`, prove that `dy/dx = |(f'(x), g'(x), h'(x)),(l,m, n),(a,b,c)|`.


Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0


If y = tan(x + y), find `("d"y)/("d"x)`


Let f(x)= |cosx|. Then, ______.


If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.


COLUMN-I COLUMN-II
(A) If a function
f(x) = `{((sin3x)/x, "if"  x = 0),("k"/2",",  "if"  x = 0):}`
is continuous at x = 0, then k is equal to
(a) |x|
(B) Every continuous function is differentiable (b) True
(C) An example of a function which is continuous
everywhere but not differentiable at exactly one point
(c) 6
(D) The identity function i.e. f (x) = x ∀ ∈x R
is a continuous function
(d) False

cos |x| is differentiable everywhere.


`cos(tan sqrt(x + 1))`


`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`


`tan^-1 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`


For the curve `sqrt(x) + sqrt(y)` = 1, `"dy"/"dx"` at `(1/4, 1/4)` is ______.


The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.


If `"f"("x") = ("sin" ("e"^("x"-2) - 1))/("log" ("x" - 1)), "x" ne 2 and "f" ("x") = "k"` for x = 2, then value of k for which f is continuous is ____________.


`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to


If `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`


Let c, k ∈ R. If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ... + f(20))| is equal to ______.


Let f: R→R and f be a differentiable function such that f(x + 2y) = f(x) + 4f(y) + 2y(2x – 1) ∀ x, y ∈ R and f’(0) = 1, then f(3) + f’(3) is ______.


If f(x) = `{{:((sin(p  +  1)x  +  sinx)/x,",", x < 0),(q,",", x = 0),((sqrt(x  +  x^2)  -  sqrt(x))/(x^(3//2)),",", x > 0):}`

is continuous at x = 0, then the ordered pair (p, q) is equal to ______.


If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.


Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.


Differentiability determines whether a function has what at a particular point?


Which expression defines the derivative of a real function \[f\] at a point \[c\] in its domain?


What is \[\frac{d}{dx}(x^n)\]?


What is \[\frac{d}{dx}(\sin x)\]?


What is \[\frac{d}{dx}(\tan x)\]?


When is a function differentiable on an open interval \[(a,b)\]?


Which conclusion establishes that \[f\] is continuous at \[x=c\]?


For \[f(x)=|x|\], what is the right-hand derivative at \[x=0\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×