हिंदी

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

Advertisements
Advertisements

प्रश्न

Differentiate the function with respect to x.

sin (x2 + 5)

योग
Advertisements

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
  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 1 | पृष्ठ १६६

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Differentiate the function with respect to x.

cos (sin x)


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:

(3x2 – 9x + 5)9


Differentiate the function with respect to x:

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


Differentiate the function with respect to x:

`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`


Differentiate the function with respect to x:

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


If f(x) = |x|3, show that f"(x) exists for all real x and find it.


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


If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`


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, ______.


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


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


cos |x| is differentiable everywhere.


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


sinn (ax2 + bx + c)


sinx2 + sin2x + sin2(x2)


sinmx . cosnx


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


`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 ______.


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


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 ____________.


If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` 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 ______.


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.


If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×