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: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
Differentiate the following w.r.t.x: `5^(sin^3x + 3)`
Differentiate the following w.r.t.x: `e^(log[(logx)^2 - logx^2]`
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:
`(x^3 - 5)^5/(x^3 + 3)^3`
Differentiate the following w.r.t.x: `cot(logx/2) - log(cotx/2)`
Differentiate the following w.r.t.x:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Differentiate the following w.r.t.x: log[tan3x.sin4x.(x2 + 7)7]
Differentiate the following w.r.t.x: `log[4^(2x)((x^2 + 5)/(sqrt(2x^3 - 4)))^(3/2)]`
Differentiate the following w.r.t.x: `log[(ex^2(5 - 4x)^(3/2))/root(3)(7 - 6x)]`
Differentiate the following w.r.t. x : cot–1(4x)
Differentiate the following w.r.t. x : `cot^-1[cot(e^(x^2))]`
Differentiate the following w.r.t. x :
`cos^-1(sqrt(1 - cos(x^2))/2)`
Differentiate the following w.r.t.x:
tan–1 (cosec x + cot x)
Differentiate the following w.r.t. x :
`cot^-1[(sqrt(1 + sin ((4x)/3)) + sqrt(1 - sin ((4x)/3)))/(sqrt(1 + sin ((4x)/3)) - sqrt(1 - sin ((4x)/3)))]`
Differentiate the following w.r.t. x : `sin^-1((4sinx + 5cosx)/sqrt(41))`
Differentiate the following w.r.t. x : `cos^-1((sqrt(3)cosx - sinx)/(2))`
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 : `sin^-1(2xsqrt(1 - x^2))`
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((5 -x)/(6x^2 - 5x - 3))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
Differentiate the following w.r.t. x : `(x^2 + 3)^(3/2).sin^3 2x.2^(x^2)`
Differentiate the following w.r.t. x: `x^(tan^(-1)x`
Differentiate the following w.r.t. x : (logx)x – (cos x)cotx
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sec((x^5 + y^5)/(x^5 - y^5))` = a2
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `e^((x^7 - y^7)/(x^7 + y^7)` = a
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sin((x^3 - y^3)/(x^3 + y^3))` = a3
If y = sin−1 (2x), find `("d"y)/(""d"x)`
If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`
Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x
If y = `(3x^2 - 4x + 7.5)^4, "then" dy/dx` is ______
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 ______
If f(x) = `(3x + 1)/(5x - 4)` and t = `(5 + 3x)/(x - 4)`, then f(t) is ______
If x2 + y2 - 2axy = 0, then `dy/dx` equals ______
If y = cosec x0, then `"dy"/"dx"` = ______.
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 ______
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 ______.
Differentiate `tan^-1 (sqrt((3 - x)/(3 + x)))` w.r.t. x.
Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.
