Hàm số y=tan ^{2} x/2 có đạo hàm là:...

Question

Hàm số \(y=\tan ^{2} \frac{x}{2}\)  có đạo hàm là: 

\(A.y'=\frac{\sin \frac{x}{2} }{\cos ^{3} \frac{x}{2} } .\)

\(B.y'=\frac{2\sin \frac{x}{2} }{\cos ^{3} \frac{x}{2} } . \)
\(C.y'=\frac{\sin \frac{x}{2} }{2\cos ^{3} \frac{x}{2} } . \)

\(D.y=\tan ^{3} \frac{x}{2} .\)

 

Answer 1

Chọn A
\(y'=2\tan \frac{x}{2} \frac{\frac{1}{2} }{\cos ^{2} \frac{x}{2} } =\frac{\sin \frac{x}{2} }{\cos ^{3} \frac{x}{2} } .y'=2\tan \frac{x}{2} \cdot \frac{\frac{1}{2} }{\cos ^{2} \frac{x}{2} } =\frac{\sin \frac{x}{2} }{\cos ^{3} \frac{x}{2} }  \)

Vậy \(y'=\frac{\sin \frac{x}{2} }{\cos ^{3} \frac{x}{2} } .\)