मराठी

Differentiate the function with respect to x. cos (sin x)

Advertisements
Advertisements

प्रश्न

Differentiate the function with respect to x.

cos (sin x)

बेरीज
Advertisements

उत्तर

Let, y = cos (sin x)

Let, sin x = t

∴ y = cos t

`dy/dt` = −sin t, `dt/dx` = cos x

`∴ dy/dx = dy/dt * dt/dx`

= −sin t · cos x

= −sin (sin x) cos x

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Continuity and Differentiability - Exercise 5.2 [पृष्ठ १६६]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 5 Continuity and Differentiability
Exercise 5.2 | Q 2 | पृष्ठ १६६

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Differentiate the function with respect to x.

sin (ax + b)


Differentiate the function with respect to x. 

cos x3 . sin2 (x5)


Differentiate the function with respect to x. 

`2sqrt(cot(x^2))`


Differentiate the function with respect to x:

`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`


Differentiate the function with respect to x:

`(cos^(-1)  x/2)/sqrt(2x+7)`, −2 < x < 2


If (x – a)2 + (y – b)2 = c2, for some c > 0, prove that `[1+ (dy/dx)^2]^(3/2)/((d^2y)/dx^2)` is a constant independent of a and b.


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)|`.


`"If y" = (sec^-1 "x")^2 , "x" > 0  "show that"  "x"^2 ("x"^2 - 1) (d^2"y")/(d"x"^2) + (2"x"^3 - "x") (d"y")/(d"x") - 2 = 0`


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)`


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


|sinx| is a differentiable function for every value of x.


`sin sqrt(x) + cos^2 sqrt(x)`


sinmx . cosnx


`tan^-1 (secx + tanx), - pi/2 < x < pi/2`


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


`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`


If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.


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


The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be


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 ______.


Let S = {t ∈ R : f(x) = |x – π| (e|x| – 1)sin |x| is not differentiable at t}. Then the set S is equal to ______.


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


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


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


Which limit is the left-hand derivative at \[x=c\]?


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


For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[a\]?


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


Why is \[|x|\] not differentiable at \[x=0\]?


When does a derivative exist?


What does differentiability at a point mean?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×