题目内容
求下列函数的导数.(1)y=2xsin(2x-5);(2)f(x)=ln
x2+1 |
分析:(1)对y=2xsin(2x-5)求导,要用到乘积的导数公式以及复合函数的求导公式;
(2)对f(x)=ln
的求导,用复合函数的求导公式求导即可.
(2)对f(x)=ln
x2+1 |
解答:解:(1)y'=(2x)'sin(2x-5)+2x[sin(2x-5)]′
=2sin(2x-5)+2x(2x-5)′cos(2x-5)
=2sin(2x-5)+4xcos(2x-5)
(2)f'(x)=
(
)′
=
.
(x2+1)-
(x2+1)′
=
.2x
=
.
=2sin(2x-5)+2x(2x-5)′cos(2x-5)
=2sin(2x-5)+4xcos(2x-5)
(2)f'(x)=
1 | ||
|
x2+1 |
=
1 | ||
|
1 |
2 |
1 |
2 |
=
1 |
2(x2+1) |
=
x |
x2+1 |
点评:本题考查简单复合函数导数,求解本题的关键是熟练掌握复合函数的求导公式及乘积的求导公式,导数由于其应用广泛性在高考中越来越受到重视,对求导公式一定要熟练掌握,记忆准确.
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