हिंदी

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

Advertisements
Advertisements

प्रश्न

Differentiate the function with respect to x.

cos (sin x)

योग
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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Continuity and Differentiability - Exercise 5.2 [पृष्ठ १६६]

APPEARS IN

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

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Differentiate the function with respect to x.

sin (ax + b)


Differentiate the function with respect to x. 

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


Differentiate the function with respect to x:

(3x2 – 9x + 5)9


Differentiate the function with respect to x:

`x^(x^2 -3) + (x -3)^(x^2)`, for x > 3


Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?


If f(x) = x + 1, find `d/dx (fof) (x)`


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)`


Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`


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


Show that the function f(x) = |sin x + cos x| is continuous at x = π.


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


`sin^-1  1/sqrt(x + 1)`


`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`


`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`


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


If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0


If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.


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 ____________.


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 ______.


A particle is moving on a line, where its position S in meters is a function of time t in seconds given by S = t3 + at2 + bt + c where a, b, c are constant. It is known that at t = 1 seconds, the position of the particle is given by S = 7 m. Velocity is 7 m/s and acceleration is 12 m/s2. The values of a, b, c are ______.


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 ______.


The set of all points where the function f(x) = x + |x| is differentiable, is ______.


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


If \[u\] and \[v\] are differentiable functions, what is \[(uv)'\]?


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


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


For \[x\ne c\], which identity is used to prove that differentiability implies continuity?


Which statement correctly describes the converse of “differentiability implies continuity”?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×