English

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

Advertisements
Advertisements

Question

Differentiate the function with respect to x.

cos (sin x)

Sum
Advertisements

Solution

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
  Is there an error in this question or solution?
Chapter 5: Continuity and Differentiability - Exercise 5.2 [Page 166]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 5 Continuity and Differentiability
Exercise 5.2 | Q 2 | Page 166

RELATED QUESTIONS

Differentiate the function with respect to x.

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


Differentiate the function with respect to x. 

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


Differentiate the function with respect to x.

`cos (sqrtx)`


Prove that the function f given by f(x) = |x − 1|, x ∈ R is not differentiable at x = 1.


Differentiate the function with respect to x:

`(5x)^(3cos 2x)`


Differentiate the function with respect to x:

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


Differentiate the function with respect to x:

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


Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/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.


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


If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`


`"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`


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


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


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


`sin^-1  1/sqrt(x + 1)`


(sin x)cosx 


(x + 1)2(x + 2)3(x + 3)4


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


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


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


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


A function is said to be continuous for x ∈ R, if ____________.


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 ______.


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


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


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


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×