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Giải bài 11 trang 68 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Đạo hàm của hàm số \(y = {\rm{si}}{{\rm{n}}^2}2x + {e^{{x^2} - 1}}\) là

ꦺ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

Đạo hàm của hàm số \(y = {\rm{si}}{{\rm{n}}^2}2x + {e^{{x^2} - 1}}\) là

A. \(y' = {\rm{sin}}4x + 2x{e^{{x^2} - 1}}\).

C. \(y' = 2{\rm{sin}}4x + 2x{e^{{x^2} - 1}}\).

B. \(y' = 2{\rm{sin}}2x + 2x{e^{{x^2} - 1}}\).

D. 💟\(y' = 4{\rm{sin}}2x{\rm{cos}}2x + {e^{{x^2} - 1}}\).

Phương pháp giải - Xem chi tiết

Áp dụng quy tắc tính đạo hàm và công thức nhân đôi \({\left( {\sin u} \right)^\prime } = u'.\cos u\);\({\left( {{e^u}} \right)^\prime } = u'.{e^u}\) \({\left( {{{\sin }^n}u} \right)^\prime } = nu'.\cos u.{\sin ^{n - 1}}u\) \(\sin 2u = 2\sin u.\cos u\)

Lời giải chi tiết

\(y = {\rm{si}}{{\rm{n}}^2}2x + {e^{{x^2} - 1}} \Rightarrow y' = 2{\rm{sin}}2x{\left( {{\rm{sin}}2x} \right)^\prime } + {\left( {{x^2} - 1} \right)^\prime }{e^{{x^2} - 1}} = 2{\rm{sin}}2x.2c{\rm{os2x}} + 2x{e^{{x^2} - 1}} = 2\sin 4x + 2x{e^{{x^2} - 1}}\)

Chọn B

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

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