cho hàm số y=f(x) = căn ( tanx+cotx) giá trị f'(pi/4)

* Hướng dẫn giải

Chọn B

$\begin{array}{l}y\text{'}=\frac{1}{2\sqrt{\tan x\text{}+\text{\hspace{0.17em}}\cot x}}.(\text{}\tan x+\cot x)\text{'}\\ =\frac{1}{2\sqrt{\tan x\text{}+\text{\hspace{0.17em}}\cot x}}.\left(\frac{1}{{\text{cos}}^{2}x}-\frac{1}{{\sin }^{2}x}\right)\\ \Rightarrow y\text{'}\left(\frac{\pi }{4}\right)=\frac{1}{2\sqrt{1+1}}.\left(\frac{1}{\frac{1}{2}}-\frac{1}{\frac{1}{2}}\right)=0\end{array}$