Giải pt đạo hàm 1) y= x⁴-2x³+5x²-x+9 2) y= 4x⁵(x³-2x²+5) 3) y= (2x⁴+9x) √x 4) y=√3x²-2x 5) y= (1+x)⁴

Đáp án:

 `1, y= x⁴ -2x³ +5x² -x +9`

`=> y’ =4x³ -6x² +10x -1`

___________________________

`2, y= 4x^5 (x³ -2x² +5)`

`=> y= 4x^8 -8x^7 +20x^5`

`=> y’ = 32x^7 -56x^6 +100x^4`

___________________________

`3, y= (2x^4 +9x).\sqrt{x}`

`=>y’ =(8x³ +9)\sqrt{x} + \frac{1}{2\sqrt{x}} .(2x⁴+9x)`

`=> y’ = 8x³\sqrt{x} +9\sqrt{x} + \frac{(2x³+9)\sqrt{x}}{2}`

`=> y’ = 8x³\sqrt{x} +9\sqrt{x} + x³\sqrt{x} + \frac{9\sqrt{x}}{2}`

`=> y’ = 9x³\sqrt{x} + \frac{27\sqrt{x}}{2}`

___________________________

`4, y=\sqrt{3x² -2x}`

`=> y’ =\frac{6x-2}{2\sqrt{3x²-2x}}`

`=> y’ =\frac{3x -1}{\sqrt{3x²-2x}}`

___________________________

`5, y= (1+x)^4`

`=> y’ = 4.(1+x)^3 .(1+x)^’`

`=> y’ = 4.(1+x)^3`

`=> y’ =4.(1+3x +3x²+x³)`

`=> y’ =4 +12x +12x² +4x³`