Advertisements
Advertisements
प्रश्न
(x + 1)2(x + 2)3(x + 3)4
उत्तर
Let y = (x + 1)2(x + 2)3(x + 3)4
∴ log y = `log [(x + 1)^2 * (x + 2)^3 (x + 3)^4]`
= `2log (x + 1) + 3 log (x + 2) + 4 log (x + 3)`
Differentiating w.r.t. x both sides, we get
`1/y * "dy"/"dx" = 2/(x + 1) + 3/(x + 2) + 4/(x + 3)`
∴ `"dy"/"dx" = y[2/(x + 1) + 3/(x + 2) + 4/(x + 3)]`
= `(x + 1)^2 * (x + 2)^3 * (x + 3)^4 [2/((x + 1)) + 3/((x + 2)) + 4/((x + 3))]`
= `(x + 1)^2 * (x + 2)^3 * (x + 3)^4 xx [(2(x + 3)(x + 3) + 3(x + 1)(x + 3) + 4(x + 1)(x + 2))/((x + 1)(x + 2)(x + 3))]`
= (x + 1)(x + 2)2(x + 3)3[9x2 + 34x + 29]
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
cos (sin x)
Prove that the function f given by `f(x) = |x - 1|, x in R` is not differentiable at x = 1.
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 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 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 y = tan(x + y), find `("d"y)/("d"x)`
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)`
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 |
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
`cos(tan sqrt(x + 1))`
`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)`
The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.
A function is said to be continuous for x ∈ R, if ____________.
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) = | cos x |, then `f((3π)/4)` is ______.
