Advertisements
Advertisements
प्रश्न
Differentiate the function with respect to x:
(3x2 – 9x + 5)9
Advertisements
उत्तर
Let, y = (3x2 – 9x + 5)9
On differentiating with respect to x,
`dy/dx = d/dx (3x^2 - 9x + 5)^9`
= `9 (3x^2 - 9x + 5)^(9 - 1) d/dx (3x^3 - 9x + 5)`
= 9(3x2 – 9x + 5)8 ⋅ (6x – 9)
= 27(3x2 – 9x + 5)8 ⋅ (2x – 3)
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
cos (sin x)
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)`
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
Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.
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 ______.
| 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 |
cos |x| is differentiable everywhere.
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
sinn (ax2 + bx + c)
`sin^-1 1/sqrt(x + 1)`
sinmx . cosnx
`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 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
`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
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 ____________.
If sin y = x sin (a + y), then value of dy/dx is
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 ______.
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
If f(x) = | cos x |, then `f((3π)/4)` is ______.
