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 x3 . sin2 (x5)
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 sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
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
If y = tan(x + y), find `("d"y)/("d"x)`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
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 |
cos |x| is differentiable everywhere.
`sin^-1 1/sqrt(x + 1)`
(sin x)cosx
sinmx . cosnx
(x + 1)2(x + 2)3(x + 3)4
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
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 ____________.
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 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 ______.
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 ______.
The function f(x) = x | x |, x ∈ R is differentiable ______.
If f(x) = | cos x |, then `f((3π)/4)` is ______.
Differentiability determines whether a function has what at a particular point?
What is \[\frac{d}{dx}(\tan x)\]?
What is the practical condition for differentiability at a point?
For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[b\]?
If \[f\] is differentiable at \[c\], which limit equals \[f'(c)\]?
For \[x\ne c\], which identity is used to prove that differentiability implies continuity?
For \[f(x)=|x|\], what is the right-hand derivative at \[x=0\]?
Why is \[|x|\] not differentiable at \[x=0\]?
When does a derivative exist?
