Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t.x:
`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
Advertisements
उत्तर
Let y = `(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
Differentiating w.r.t. x,we get,
`"dy"/"dx" = "d"/"dx"(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
`= 5(sqrt(3x - 5) - 1/sqrt(3x - 5))^4."d"/"dx"(sqrt(3x - 5) - 1/sqrt(3x - 5))`
`= 5(sqrt(3x - 5) - 1/sqrt(3x - 5))^4.["d"/"dx"(3x - 5)^(1/2) - "d"/"dx"(3x - 5)^(-1/2))]`
`= 5(sqrt(3x - 5) - 1/sqrt(3x - 5))^4. [1/2(3x - 5)^(-1/2)."d"/"dx"(3x - 5) - (-1/2)(3x - 5)^(-3/2)."d"/"dx"(3x - 5)]`
`= 5(sqrt(3x - 5) - 1/sqrt(3x - 5))^4. [1/(2sqrt(3x - 5)).(3 × 1 - 0) + 1/(2(3x - 5)^(3/2)).(3 × 1 - 0)]`
`= 5(sqrt(3x - 5) - 1/sqrt(3x - 5))^4. [3/(2(3x - 5)^(1/2)) +3/(2(3x - 5)^(3/2))]`
`= 5(sqrt(3x - 5) - 1/sqrt(3x - 5))^4. 3/2 [1/(3x - 5)^(1/2) + 1/(3x - 5)^(3/2)]`
`= 15/2 (sqrt(3x - 5) - 1/sqrt(3x - 5))^4. [(1 × (3x - 5))/((3x - 5)^(1/2) × (3x - 5)^1) + 1/(3x - 5)^(3/2)]`
`= 15/2 (sqrt(3x - 5) - 1/sqrt(3x - 5))^4. [(1 × (3x - 5))/((3x - 5)^(1/2 + 1)) + 1/(3x - 5)^(3/2)]`
`= 15/2 (sqrt(3x - 5) - 1/sqrt(3x - 5))^4. [(3x - 5)/((3x - 5)^(3/2)) + 1/(3x - 5)^(3/2)]`
`= 15/2 (sqrt(3x - 5) - 1/sqrt(3x - 5))^4. [(3x - 5 + 1)/((3x - 5)^(3/2))]`
`= (15(3x - 4))/(2(3x - 5)^(3/2))(sqrt(3x - 5) - 1/sqrt(3x - 5))^4`.
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t. x: `sqrt(x^2 + 4x - 7)`.
Differentiate the following w.r.t.x:
`sqrt(x^2 + sqrt(x^2 + 1)`
Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
Differentiate the following w.r.t.x: `sqrt(tansqrt(x)`
Differentiate the following w.r.t.x: cot3[log(x3)]
Differentiate the following w.r.t.x: cos2[log(x2 + 7)]
Differentiate the following w.r.t.x: `sinsqrt(sinsqrt(x)`
Differentiate the following w.r.t.x:
sin2x2 – cos2x2
Differentiate the following w.r.t.x:
(x2 + 4x + 1)3 + (x3− 5x − 2)4
Differentiate the following w.r.t.x: `x/(sqrt(7 - 3x)`
Differentiate the following w.r.t.x: (1 + sin2 x)2 (1 + cos2 x)3
Differentiate the following w.r.t.x:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Differentiate the following w.r.t.x:
y = (25)log5(secx) − (16)log4(tanx)
Differentiate the following w.r.t. x:
`(x^2 + 2)^4/(sqrt(x^2 + 5)`
Differentiate the following w.r.t. x:
`sin^-1(sqrt((1 + x^2)/2))`
Differentiate the following w. r. t. x.
cos–1(1 – x2)
Differentiate the following w.r.t. x :
cos3[cos–1(x3)]
Differentiate the following w.r.t. x : `tan^-1[(1 + cos(x/3))/(sin(x/3))]`
Differentiate the following w.r.t. x : `tan^-1(sqrt((1 + cosx)/(1 - cosx)))`
Differentiate the following w.r.t. x : `cos^-1((3cos3x - 4sin3x)/5)`
Differentiate the following w.r.t. x :
`cos^-1[(3cos(e^x) + 2sin(e^x))/sqrt(13)]`
Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`
Differentiate the following w.r.t. x :
`cos^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `tan^-1((2x)/(1 - x^2))`
Differentiate the following w.r.t. x : cos–1(3x – 4x3)
Differentiate the following w.r.t. x :
`sin^-1(4^(x + 1/2)/(1 + 2^(4x)))`
Differentiate the following w.r.t. x :
`sin^(−1) ((1 − x^3)/(1 + x^3))`
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Differentiate the following w.r.t. x : `tan^-1((2^x)/(1 + 2^(2x + 1)))`
Differentiate the following w.r.t. x : `cot^-1((a^2 - 6x^2)/(5ax))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
Differentiate the following w.r.t. x: `x^(tan^(-1)x`
Differentiate the following w.r.t. x : `[(tanx)^(tanx)]^(tanx) "at" x = pi/(4)`
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : x7.y5 = (x + y)12
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `tan^-1((3x^2 - 4y^2)/(3x^2 + 4y^2))` = a2
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `cos^-1((7x^4 + 5y^4)/(7x^4 - 5y^4)) = tan^-1a`
Differentiate sin2 (sin−1(x2)) w.r. to x
Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x
The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t2 + 3 and w = t2 - t + 2, then the rate of change of W with respect to t at t = 1 is ______
The volume of a spherical balloon is increasing at the rate of 10 cubic centimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is 4 centimetres, is ______
If x = p sin θ, y = q cos θ, then `dy/dx` = ______
The value of `d/(dx)[tan^-1((a - x)/(1 + ax))]` is ______.
If x = eθ, (sin θ – cos θ), y = eθ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.
Let f(x) be a polynomial function of the second degree. If f(1) = f(–1) and a1, a2, a3 are in AP, then f’(a1), f’(a2), f’(a3) are in ______.
