मराठी

Differentiate the function with respect to x. sin (x2 + 5) - Mathematics

Advertisements
Advertisements

प्रश्न

Differentiate the function with respect to x.

sin (x2 + 5)

बेरीज

उत्तर

Let, y = sin (x2 + 5)

On differentiating with respect to x,

`"dy"/"dx" = "d"/"dx" sin (x^2 + 5)`

`= cos (x^2 + 5) "d"/"dx" (x^2 + 5)`

= cos (x2 + 5)(2x + 0)

= 2x cos (x2 + 5).

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

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Differentiate the function with respect to x.

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


Differentiate the function with respect to x. 

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


Differentiate the function with respect to x. 

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


Differentiate w.r.t. x the function:

sin3 x + cos6 x


Differentiate w.r.t. x the function:

`sin^(–1)(xsqrtx ), 0 ≤ x ≤ 1`


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.


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)|`


Discuss the continuity and differentiability of the 

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

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)`


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

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


sinn (ax2 + bx + c)


sinmx . cosnx


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


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


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 ____________.


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))`


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 ______.


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.


The function f(x) = x | x |, x ∈ R is differentiable ______.


If f(x) = | cos x |, then `f((3π)/4)` is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×