Advertisements
Advertisements
प्रश्न
sinx2 + sin2x + sin2(x2)
Advertisements
उत्तर
Let sinx2 + sin2x + sin2(x2)
∴ `"dy"/"dx" = "d"/"dx" sin(x^2) + "d"/"dx" (sinx)^2 + "d"/"dx" (sin x^2)^2`
= `cos(x^2) "d"/"dx" (x^2) + 2 sinx * "d"/"dx" (sin x) + 2 sinx^2 "d"/"dx" (sin x^2)`
= `2x cosx^2 + 2 sin x cos x + 2sinx^2 cosx^2 "d"/"dx" x^2`
= `2x cosx^2 + 2 sin x cos x + 2 sin x^2 cos x^2 xx 2x`
= 2x cos(x2) + sin 2x + 2x sin 2(x2)
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
sin (x2 + 5)
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)`
Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.
Discuss the continuity and differentiability of the
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
Let f(x)= |cosx|. Then, ______.
Differential coefficient of sec (tan–1x) w.r.t. x 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.
`sin^-1 1/sqrt(x + 1)`
(x + 1)2(x + 2)3(x + 3)4
`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 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
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 ______.
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 ____________.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is
If sin y = x sin (a + y), then value of 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 ______.
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 set of all points where the function f(x) = x + |x| is differentiable, is ______.
