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

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1. Đáp án:

    `1, y= x⁴ -2x³ +5x² -x +9`

   `=> y’ =4x³ -6x² +10x -1`

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   `2, y= 4x^5 (x³ -2x² +5)`

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

   `=> y’ = 32x^7 -56x^6 +100x^4`

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   `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}`

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   `4, y=\sqrt{3x² -2x}`

   `=> y’ =\frac{6x-2}{2\sqrt{3x²-2x}}`

   `=> y’ =\frac{3x -1}{\sqrt{3x²-2x}}`

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   `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`

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2. 1). y’ = 4x³ – 6x² + 10x – 1

   2). y’ = (4x⁵)'(x³ – 2x² + 5) + (x³ – 2x² + 5)’4x⁵

             = 20x⁴ (x³ – 2x² + 5) + (3x² -4x)4x⁵

             = 20x⁷ – 40x⁶ + 100x⁴ +12x⁷ – 16x⁶

             = 32x⁷ – 56x⁶ +100 x⁴

   5). y’ = 4 (1 + x)'(1 + x)³ 

             = 4 (1 + x)³

    

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