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Giải bài 9.11 trang 60 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Tính đạo hàm của hàm số \(y = 3\tan \left( {x + \frac{\pi }{4}} \right) - 2\cot \left( {\frac{\pi }{4} - x} \right)\).

🅰Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Tính đạo hàm của hàm số \(y = 3\tan \left( {x + \frac{\pi }{4}} \right) - 2\cot \left( {\frac{\pi }{4} - x} \right)\).

Phương pháp giải - Xem chi tiết

Áp dụng quy tắc đạo hàm của hàm số lượng giác và hàm hợp

\({\left( {\tan u} \right)^\prime } = \frac{{u'}}{{{{\cos }^2}u}};{\left( {\cot u} \right)^\prime } =  - \frac{{u'}}{{{{\sin }^2}u}};\)

Lời giải chi tiết

\(y' = \frac{3}{{{{\cos }^2}\left( {x + \frac{\pi }{4}} \right)}} - \frac{2}{{{{\sin }^2}\left( {\frac{\pi }{4} - x} \right)}} = \frac{1}{{{{\cos }^2}\left( {x + \frac{\pi }{4}} \right)}} = 1 + {\tan ^2}\left( {x + \frac{\pi }{4}} \right)\).

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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