Giúp mik vs ạ $\overline x$,$=4x+\frac2{x^2}+\frac1{2\sqrt x}$,Bài 3: Tính đạo hàm,$a,~y=(2x-4).(6-3x)$,$b,~y=(x^4-4x^3+2).(x-4)$,$c)~y=(3x^2+6x-2).(x^2-9x)$,$d,~y=(3x^2-6x+8).(x^4-9)$,$e)~y=(x^5-3x^2+x).(x-6)$,$g,~y=(\frac32x^2+2x-6).(4x+6)$,HONG

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Accepted Answer

{"userId":5332128,"userName":"Trần My"}

Bài 2: Tính đạo hàm (rút gọn nếu có)

a) y = (x^2 + 1) / sqrt(x^2 + 1) = sqrt(x^2 + 1)

y' = (2x) / (2 * sqrt(x^2 + 1)) = x / sqrt(x^2 + 1)

b) y = (x^4 - 4x^3 + 1)(x - 4)

y' = (4x^3 - 12x^2)(x - 4) + (x^4 - 4x^3 + 1)(1)

y' = 4x^4 - 16x^3 - 12x^3 + 48x^2 + x^4 - 4x^3 + 1

y' = 5x^4 - 32x^3 + 48x^2 + 1

c) y = (3x^2 + 6x - 1)(x^2 - 9)

y' = (6x + 6)(x^2 - 9) + (3x^2 + 6x - 1)(2x)

y' = 6x^3 - 54x + 6x^2 - 54 + 6x^3 + 12x^2 - 2x

y' = 12x^3 + 18x^2 - 56x - 54

d) y = (x^5 - 3x + 8)(x - 6)

y' = (5x^4 - 3)(x - 6) + (x^5 - 3x + 8)(1)

y' = 5x^5 - 30x^4 - 3x + 18 + x^5 - 3x + 8

y' = 6x^5 - 30x^4 - 6x + 26

e) y = (3x^2 + 2x - 6) / (4x + 6)

y' = ((6x + 2)(4x + 6) - (3x^2 + 2x - 6)(4)) / (4x + 6)^2

y' = (24x^2 + 36x + 8x + 12 - 12x^2 - 8x + 24) / (4x + 6)^2

y' = (12x^2 + 36x + 36) / (4x + 6)^2 = (12(x^2 + 3x + 3)) / (4(2x + 3)^2) = (3(x^2 + 3x + 3)) / (2x + 3)^2

f) y = (x^3 - 2x^2 + 1) / (x^2 + 1)

y' = ((3x^2 - 4x)(x^2 + 1) - (x^3 - 2x^2 + 1)(2x)) / (x^2 + 1)^2

y' = (3x^4 + 3x^2 - 4x^3 - 4x - 2x^4 + 4x^3 - 2x) / (x^2 + 1)^2

y' = (x^4 + 3x^2 - 6x) / (x^2 + 1)^2

g) y = (x^2 - 3x + 2) / (x - 1) = ((x - 1)(x - 2)) / (x - 1) = x - 2 (với x khác 1)

y' = 1 (với x khác 1)