English

Differentiate the function with respect to x. cos⁡(√𝑥)

Advertisements
Advertisements

Question

Differentiate the function with respect to x.

`cos (sqrtx)`

Sum
Advertisements

Solution

Let, y = cos `(sqrtx)`

`dy/dx = d/dx cos (sqrtx)`

= `-sin sqrtx. d/dx (sqrtx)`

= `-sin sqrtx . 1/2 (x)^((-1)/2)`

= `(-sin sqrtx)/(2sqrtx)`

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 8 | Page 166

RELATED QUESTIONS

Differentiate the function with respect to x.

sin (ax + b)


Differentiate the function with respect to x. 

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


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:

`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`


Discuss the continuity and differentiability of the 

\[f\left( x \right) = \left| x \right| + \left| x - 1 \right| \text{in the interval} \left( - 1, 2 \right)\]

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


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


sinx2 + sin2x + sin2(x2)


(sin x)cosx 


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


`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`


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


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


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 ____________.


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


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


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?


If \[u\] and \[v\] are differentiable functions, which formula is correct?


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


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


A function is differentiable at \[x=c\] when which condition holds?


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


What is the practical condition for differentiability at a point?


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


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


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


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


When does a derivative exist?


What does differentiability at a point mean?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×