Advertisements
Advertisements
प्रश्न
(x + 1)2(x + 2)3(x + 3)4
Advertisements
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)
Differentiate the function with respect to x.
sin (ax + b)
Differentiate the function with respect to x:
(3x2 – 9x + 5)9
Differentiate the function with respect to x:
`(5x)^(3cos 2x)`
If f(x) = |x|3, show that f"(x) exists for all real x and find it.
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
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)|`.
Discuss the continuity and differentiability of the
If f(x) = x + 1, find `d/dx (fof) (x)`
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 ______.
cos |x| is differentiable everywhere.
`cos(tan sqrt(x + 1))`
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`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
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"])` ____________.
The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is
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 ______.
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
What is \[\frac{d}{dx}(\sin x)\]?
A function is differentiable at \[x=c\] when which condition holds?
Which limit is the right-hand derivative at \[x=c\]?
What is the practical condition for differentiability at a point?
If \[f\] is differentiable at \[c\], which limit equals \[f'(c)\]?
Which conclusion establishes that \[f\] is continuous at \[x=c\]?
Why is \[|x|\] not differentiable at \[x=0\]?
When does a derivative exist?
