单选题
设y=(1+sin x)
x
，则dy∣
x=π
=
【正确答案】
A
【答案解析】解析：因y=(1+sin x)
x
=e
xln(1+sin x)
，则 dy=e
xln(1+sin x)
d[xln(1+sin x)] =(1+sin x)
x
{ln(1+sin x)dx+xd[ln(1+sin x)]} =(1+sin x)
x
[1n(1+sin x)dx+
d(sin x)] =(1+sin x)
x
[1n(1+sin x)dx+
dx] =(1+sin x)
x
[ln(1+sin x)+
]dx， 所以dy∣
x=π
=(1+sinπ)
x
ln(1+sinπ)+
d(sin x)] =(1+sin x)
x
[1n(1+sin x)dx+
dx] =(1+sin x)
x
[ln(1+sin x)+
]dx， 所以dy∣
x=π
=(1+sinπ)
x
ln(1+sinπ)+