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: `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: cos(x2 + a2)
Differentiate the following w.r.t.x: `"cosec"(sqrt(cos x))`
Differentiate the following w.r.t.x:
tan[cos(sinx)]
Differentiate the following w.r.t.x: sec[tan (x4 + 4)]
Differentiate the following w.r.t.x: `sinsqrt(sinsqrt(x)`
Differentiate the following w.r.t.x: `log[sec (e^(x^2))]`
Differentiate the following w.r.t.x: `log_(e^2) (log x)`
Differentiate the following w.r.t.x:
`sqrt(cosx) + sqrt(cossqrt(x)`
Differentiate the following w.r.t.x:
log (sec 3x+ tan 3x)
Differentiate the following w.r.t.x: `log(sqrt((1 - sinx)/(1 + sinx)))`
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:
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 : cosec–1 (e–x)
Differentiate the following w.r.t. x : cot–1(4x)
Differentiate the following w.r.t. x : `sin^4[sin^-1(sqrt(x))]`
Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`
Differentiate the following w.r.t. x : `"cosec"^-1((1)/(4cos^3 2x - 3cos2x))`
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 : `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) ((1 − x^3)/(1 + x^3))`
Differentiate the following w.r.t. x :
`tan^(−1)[(2^(x + 2))/(1 − 3(4^x))]`
Differentiate the following w.r.t. x : `cot^-1((a^2 - 6x^2)/(5ax))`
Differentiate the following w.r.t. x : `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2)`
Differentiate the following w.r.t. x : (sin x)x
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
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
If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`
Differentiate sin2 (sin−1(x2)) w.r. to x
If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`
If the function f(x) = `(log (1 + "ax") - log (1 - "bx))/x, x ≠ 0` is continuous at x = 0 then, f(0) = _____.
Derivative of (tanx)4 is ______
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.
Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.
