Bạn đang xem: Bài 3 trang 163 toán 11
" data-position="bottom" id="navbar" class="navbar-collapse collapse" aria-expanded="false" style="height: 1px;"> // reviews // hệ thống bài kiểm tra // // // // // // thông tin cung cấpBài 3 (trang 163 SGK Đại số 11):Tìm đạo hàm của các hàm số sau :
Bài giải:
a) biện pháp 1 :
y’ = <(x7- 5x2)3>'
= <(x7)3– 3.(x7)2.5x2+ 3.x7.(5x2)2– (5x2)3>’
= (x21– 15.x16+ 75x11– 125x6)’
= (x21)’ – (15x16)’ + (75x11)’ – (125x6)’
= 21x20– 15.16x15+ 75.11x10– 125.6x5
= 21x20– 240x15+ 825x10– 750x5.
Cách 2 :
y’ = <(x7- 5x2)3>'
= 3.(x7– 5x2)2.(x7– 5x2)’ (Đạo hàm của hàm hợp với u = x7– 5x2; y = u3)
= 3.(x7– 5x2)2.< (x7)’ – (5x2)’>
= 3.(x7– 5x2)2(7x6– 5.2x)
= 3.(x7– 5x2)2(7x6– 10x)
b) y’ = <(x2+ 1)(5 – 3x2)>’
= (x2+ 1)’.(5 – 3x2) + (x2+ 1)(5 – 3x2)’ (Đạo hàm của tích)
= <(x2)’ + (1)’>(5 – 3x2) + (x2+ 1)<(5)’ – (3x2)’>
= (2x + 0)(5 – 3x2) + (x2+ 1)(0 – 3.2x)
= 2x.(5 – 3x2) + (x2+ 1).(-6x)
= 2x.5 – 2x.3x2+ x2(-6x) + 1(-6x)
= 10x – 6x3– 6x3– 6x
= -12x3+ 4x.
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