đạo hàm

C

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%%- Giải:

a) $y' = (\frac{x^5 - 3}{\sqrt{x^3}})' = \frac{(x^5 - 3)'\sqrt{x^3} - (x^5 - 3)(\sqrt{x^3})'}{(\sqrt{x^3})^2}$

$= \frac{5x^5\sqrt{x} - (x^5 - 3)\frac{3x}{2\sqrt{x}}}{x^3}$


b) $y = (a + \frac{b}{x} + \frac{c}{x^2})^4$

Đặt $u = a + \frac{b}{x} + \frac{c}{x^2}$ \Rightarrow $u'_x = \frac{-b}{x^2} - \frac{2c}{x^3}$

Khi đó:$ y = u^4$ \Rightarrow $y'_u = 4u^3 = 4( a + \frac{b}{x} + \frac{c}{x^2})^3$

Vậy: $y'_x = u'_x.y'_u =4(\frac{-b}{x^2} - \frac{2c}{x^3})(a + \frac{b}{x} + \frac{c}{x^2})^3$







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