Giải câu 3 bài 2: Quy tắc tính đạo hàm.
a) y=(x7−5x2)3
y′=3.(x7−5x2)2.(x7−5x2)′
=3.(x7−5x2)2.(7x6−10x)
=3x5.(x5−5)2(7x5−10)
b) y=(x2+1)(5−3x2)
=5x2−3x4+5−3x2
=−3x4+2x2+5
y′=−12x3+4x=−4x.(3x2−1).
c) y=2xx2−1
y′=(2x)′.(x2−1)−2x(x2−1)′(x2−1)2
=2.(x2−1)−2x.2x(x2−1)2
=−2(x2+1)(x2−1)2
d) y=3−5xx2−x+1
y′=(3−5x)′(x2−x+1)−(3−5x).(x2−x+1)′(x2−x+1)2
=−5(x2−x+1)−(3−5x).(2x−1)(x2−x+1)2
=−5x2+5x−5−6x+3+10x2−5x(x2−x+1)2
=5x2−6x−2(x2−x+1)2.
e) y=(m+nx2)3 (m,n là các hằng số)
y′=3.(m+nx2)2.(m+nx2)′
=3.(m+nx2)2(−2nx3)
=−6nx3.(m+nx2)2.
