Bài 2 trang 61 sgk giải tích 12: Bài 2. Hàm số lũy thừa...

Bài 2. Tìm các đạo hàm của các hàm số:

a) $y= \left ( 2x^{2} -x+1\right )^{\frac{1}{3}}$;

b) $y= \left ( 4-x-x^{2}\right )^{\frac{1}{4}}$;

c) $y= \left ( 3x+1\right )^{\frac{\pi }{2}}$;

d) $y= \left ( 5-x\right )^{\sqrt{3}}$.

a)  $y^{‘}=\frac{1}{3}\left ( 2x^{2} -x+1\right )^{‘}\left (2x^{2}-x+1 \right )^{\frac{1}{3}-1}$=  $\frac{\left ( 4x-1\right )\left ( 2x^{2}-x+1 \right )^{\frac{-2}{3}}}{3}$.

b) $y^{‘}=\frac{1}{4}\left ( 4-x-x^{2} \right )^{‘}\left ( 4-x-x^{2} \right )^{\frac{1}{4}-1}$= $\frac{1}{4}\left ( -2x-1 \right )\left ( 4-x-x^{2} \right )^{\frac{-3}{4}}$.

c) $y^{‘}$= $\frac{\pi }{2}\left ( 3x+1 \right )^{‘}\left ( 3x+1 \right )^{\frac{\pi }{2}-1}$= $\frac{3\pi }{2}\left ( 3x+1 \right )^{\frac{\pi }{2}-1}$.

d) $y^{‘}$= $\sqrt{3}\left ( 5-x \right )^{‘}\left ( 5-x \right )^{\sqrt{3}-1}$= $-\sqrt{3}\left ( 5-x \right )^{\sqrt{3}-1}$.