Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t.x:
`(x^3 - 5)^5/(x^3 + 3)^3`
Advertisements
उत्तर
Let y = `(x^3 - 5)^5/(x^3 + 3)^3`
Differentiating w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"[(x^3 - 5)^5/(x^3 + 3)^3]`
`"dy"/"dx" = [(x^3 + 3)^3 × "d"/"dx"(x^3 - 5)^5 - (x^3 - 5)^5 "d"/"dx" (x^3 + 3)^3]/[(x^3 + 3)^3]^2`
`"dy"/"dx" = [(x^3 + 3)^3 × 5(x^3 - 5)^4 × "d"/"dx"(x^3 - 5) - (x^3 - 5)^5 × 3(x^3 + 3)^2 × "d"/"dx" (x^3 + 3)]/(x^3 + 3)^6`
`"dy"/"dx" = [(x^3 + 3)^3 × 5(x^3 - 5)^4 × (3x^2 - 0) - (x^3 - 5)^5 × 3(x^3 + 3)^2 × (3x^2 + 0)]/(x^3 + 3)^6`
`"dy"/"dx" = [3x^2(x^3 + 3)^2(x^3 - 5)^4[5(x^3 + 3) - 3(x^3 - 5)]]/(x^3 + 3)^6`
`"dy"/"dx" = [3x^2(x^3 + 3)^2(x^3 - 5)^4[5x^3 + 15 - 3x^3 + 15]]/(x^3 + 3)^6`
`"dy"/"dx" = [3x^2cancel((x^3 + 3)^2)(x^3 - 5)^4(2x^3 + 30)]/(x^3 + 3)^(cancel(6)4)`
`"dy"/"dx" = [3x^2(x^3 - 5)^4(2x^3 + 30)]/(x^3 + 3)^4`
`"dy"/"dx" = [3x^2(x^3 - 5)^4 . 2(x^3 + 15)]/(x^3 + 3)^4`
`"dy"/"dx" = [6x^2(x^3 + 15)(x^3 - 5)^4]/(x^3 + 3)^4`
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t. x:
(x3 – 2x – 1)5
Differentiate the following w.r.t.x:
`sqrt(x^2 + sqrt(x^2 + 1)`
Differentiate the following w.r.t.x:
`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
Differentiate the following w.r.t.x: cot3[log(x3)]
Differentiate the following w.r.t.x: (1 + 4x)5 (3 + x −x2)8
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: `log[(ex^2(5 - 4x)^(3/2))/root(3)(7 - 6x)]`
Differentiate the following w.r.t. x:
`(x^2 + 2)^4/(sqrt(x^2 + 5)`
Differentiate the following w.r.t. x : tan–1(log x)
Differentiate the following w.r.t. x : cosec–1 (e–x)
Differentiate the following w.r.t. x : `tan^-1(sqrt(x))`
Differentiate the following w. r. t. x.
cos–1(1 – x2)
Differentiate the following w.r.t. x : `cot^-1[cot(e^(x^2))]`
Differentiate the following w.r.t. x : `tan^-1[(1 - tan(x/2))/(1 + tan(x/2))]`
Differentiate the following w.r.t.x:
tan–1 (cosec x + cot x)
Differentiate the following w.r.t. x : `cos^-1((sqrt(3)cosx - sinx)/(2))`
Differentiate the following w.r.t. x : `sin^-1((cossqrt(x) + sinsqrt(x))/sqrt(2))`
Differentiate the following w.r.t. x : `cos^-1((3cos3x - 4sin3x)/5)`
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:
`tan^-1((2x^(5/2))/(1 - x^5))`
Differentiate the following w.r.t. x : `cot^-1((1 - sqrt(x))/(1 + sqrt(x)))`
Differentiate the following w.r.t. x :
`tan^(−1)[(2^(x + 2))/(1 − 3(4^x))]`
Differentiate the following w.r.t. x : `root(3)((4x - 1)/((2x + 3)(5 - 2x)^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^(x^x) + e^(x^x)`
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
Differentiate the following w.r.t. x :
etanx + (logx)tanx
Differentiate the following w.r.t. x :
(sin x)tanx + (cos x)cotx
Differentiate the following w.r.t. x : `10^(x^(x)) + x^(x(10)) + x^(10x)`
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: `log((x^20 - y^20)/(x^20 + y^20))` = 20
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 is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.
Differentiate y = `sqrt(x^2 + 5)` w.r. to x
If f(x) is odd and differentiable, then f′(x) is
If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`
If y = `tan^-1[sqrt((1 + cos x)/(1 - cos x))]`, find `("d"y)/("d"x)`
Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x
Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x
If `t = v^2/3`, then `(-v/2 (df)/dt)` is equal to, (where f is acceleration) ______
If y = `1 + x + x^2/(2!) + x^3/(3!) + x^4/(4!) + .....,` then `(d^2y)/(dx^2)` = ______
A particle moves so that x = 2 + 27t - t3. The direction of motion reverses after moving a distance of ______ units.
Find `(dy)/(dx)`, if x3 + x2y + xy2 + y3 = 81
If x = eθ, (sin θ – cos θ), y = eθ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.
Differentiate `tan^-1 (sqrt((3 - x)/(3 + x)))` w.r.t. x.
