（17）. y?arctan（19）.y?x221?x1?x2； （18）. y?arctan?tan2x?；
a2x?a?2ln(x?x?a)
22（20）. y?lnx21?x?1?x?221?x1?x；
xa（21）.y?a?x?a22arcsin；
（22）.y?sin?sin(sinx)?. 解：
（1）.y??8?x?1??.x?1??2?3x?1??.3x?1??8?x?1??6?3x?1??26x?14；
??（2）. y??7.?1?2x?6?1?2x????14(1?2x)6； （3）. y??1lnx1sine1xx?lnx???x1xlnx；
1x （4）. y??（5）.y??2ln?sine???sine.cose.ex????exxcotex；
?1ln?1??ln2?ln??2xln2??lnx?； ?x?1（6）. y??1??2x?2?2x???21?4x2；
??（7）. y???e?3x??3x??sin2x?e?3x?cos2x?2x???e?3x??3sin2x?2cos2x?；
????????（8）.
?x??cos???????1x?x?24?x??????????2y??tan?????sec???.???? ??x???x????24???24??24??tan????sin?????2424??????x??cos???11?24??..??2?x??2?xsin???cos????24??24?
?1?x?2sin???24??x??cos??????24??1?sin?x??2?????1cosx?secx.
6
（9）.y??cosln?1?1?2x?1?ln?2x?1???cosln2?2?cosln2x?1.
?1?2x?1???2x?1???2x?1?
?12x?1（10）. y??x?1x?a1x?x?a2222?x?x?a22??x??1x?a22?1221?x?a?2????x?212?a2????
? ???11?.2x???22x?2x?a??1x?a22????x?a2?x?? 22x?a??2 ??1x?a22.
（11）.y??11?sin?2x?2?sin2?x ??11?sin4?.2sinx?sinx? x ?11?sinx4.2sinxcosx?sin2x1?sinx4；
??12?1?x?? 2?21?x?（12）. y???1?1?1?x?22?1?x????21x2??
?x1?1??????2x??2x?21?x2x1?x?；
????1??x??11x?1arccosx（13）. y??1arccos??arccos1?x?11???x?arccos???1?1????? 2?1??x??1?????x?? ????1arccos?x1?11??x?1?2xxx???????2x；
（14）. y????12222?1.a?x?x.?a?x?22?2a?x????a?x22?2
???1??2x??1.a?x?x.?22?2a?x?22?a?x22?2?a2?a?x22?3
7
（15）.y???2sinx?sinx???.sinx2?sin????sin22?22x.cosx.x????????x2
??2sinxcosx?.sinx2?sin2x.?2xcosx2?sinx22222
?sin2x.sinx?2xsinx.cosxsinx2?2322；
1?1?x??（16）. y???3?3?1?x????1?x2?1????1?x3?3??3?2x.1?x3?1?x2.?3x2?32221?x??1?x?????1?x3???1?????????
??? ?133?1?x3?2x?3x2?x4??； ?1?x3?.321?x??2??（17）.
?21?x?1?x?2??y???.??2?1?x?2??1?x?2?1?x?2?1?x??1?x?1???1?x??111?x2
?；
（18）. y?arctan?tan2x?；
y??11?tan?2x?22?tan；
2x???11?tan4?2tanx?tanx??????x?
?2tanx.secx1?tanxx24（19）.y?x?a?22a22ln(x?x?a)；
22?xy????2?2a?x?a??ln(x?2?22?x?a)
2????a?????2????x?22??
??1????2x?a22x?122??x?a2?2x2?a2??1x?a22(x??x?a)???22
?1???2x?a22?a2?????2222x?a???x?x2???1?1?.2x???22?22x?a?2x?a???1
8
?x2?a2?x2?a2????222?2x?a???1x?a1?x1?x22?2x?a2?22?2?x?a.
222x?a（20）. y?ln1?x?1?x?1?x?1?x?1?x；
y?ln??ln?1?x???1?x?1?x2x?22?1?1?x??ln
x?? ?ln1?1?x2?lnx.
y??ln1?1?x????2????lnx????11?1?x2?1?1?x2??1 x? ?11?1?x2?121?x?0?221?x??????1
?x2? ?1?11?x2.x1?x2?1x?1?1?xx2.x1?x2?1x
?1?1?xx1?x22?1x?1x1?x22；
xa（21）.y??xy????2x2a?x?2a22arcsin；
??2ax???22a?x???arcsin?
2a?????a2x?12222??a?x??.a?x???2?2a2?x22???
??1????2???x???2a?x???1????a?1?
?1212a?x?22x222?a22aa?x22a?x222.1a
?a?x?aa?x222；
2a?x（22）.y?sin?sin(sinx)?.
解：y??cos?sin(sinx)?(sin(sinx))??cos?sin(sinx)?.cos(sinx).(sinx)?
?sin(sixn)?. ?cosx.cos(sinx).cos9
3． 设y?f?sinx2?，其中f?x?可导，求y?.
?2?22222解：y??f??sinx2??.sinx??f??sinx?.cosx.?x??2xcosxf??sinx?.
??????4． 设函数u?x?,v?x?可微，求下列函数的导数.
（1）y?u2?x??v2?x?，?u2?x??v2?x??0?； （2）y?arccot解： （1）y??1212u?x?v?x?,?v?c??0?.
?u.2?x??v?x??2?12.u?2?x??v2?x??
? ?1u2?x??v?x?2.?2u?x?.u??x??2v?x?.v??x??；
（2）
?2?u??x?.v?x??u?x?.v?x??v?x??u?x??y???? 2???u2?x??v2?x??2???vx??vx????u?x???1????v?x??1 ??u??x?v?x??u?x?.v?x?u2?x??v2?x?.
5．设y????ln??x???，其中??x?为正值可导函数，求y?. ???x????1?????????????x.?x?ln?x.?x??????ln??x??????x??ln??x???ln??x???? 解：y??????.??.??????2???x????x?????x?????x?????? ????x??1?ln??x???2?x??ln??x??.????. ???x??6．设y?f??2x?3?2?，f??x??arctanx?2x?3? ① ，求y??0?.
?12?2x?3??2x?3??2x?3???f.解：因为y??f??. ② .?????2?2x?3??2x?3??2x?3??2x?3?10