作业帮若f(x)=(x-1)*e^(x-1),则f’(x)怎么求
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若f(x)=(x-1)*e^(x-1),则f’(x)怎么求
若f(x)=(x-1)*e^(x-1),则f’(x)怎么求
若f(x)=(x-1)*e^(x-1),则f’(x)怎么求
f(x)=(x-1)*e^(x-1),
=x*e^(x-1)-e^(x-1)
x*e^(x-1)'=x'*e^(x-1)+x*(x-1)'*e^(x-1)
=e^(x-1)+xe^(x-1)
e^(x-1)=(x-1)'*e^(x-1)=e^(x-1)
f'(x)=xe^(x-1)
可以看成 f(y)=y*e^y
f'(x)=(y)'e^y+y(e^y)'=e^y+y(y)'e^y=(1+y)e^y
代入y=x-1
f(x)=xe^(1-x)
f'(x)＝x'*e^(x-1)+x*[e^(x-1)]'
f'(x)＝x'*e^(x-1)+x*(x-1)'*e^(x-1)
=(1+x)e^(x-1)
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