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.
`sec(tan (sqrtx))`
Differentiate the function with respect to x.
cos x3 . sin2 (x5)
Differentiate the function with respect to x.
`cos (sqrtx)`
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:
sin3 x + cos6 x
Differentiate the function with respect to x:
`(5x)^(3cos 2x)`
Differentiate the function with respect to x:
`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`
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 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)`
If y = tan(x + y), find `("d"y)/("d"x)`
Let f(x)= |cosx|. Then, ______.
If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.
|sinx| is a differentiable function for every value of x.
`cos(tan sqrt(x + 1))`
sinx2 + sin2x + sin2(x2)
`sin^-1 1/sqrt(x + 1)`
(sin x)cosx
`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`
`tan^-1 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`
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 ______.
A function is said to be continuous for x ∈ R, if ____________.
`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to
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) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
