设函数f(x)=(x-1)(x-2)...(x-100)(x>100),求F'(X)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 23:19:47
![设函数f(x)=(x-1)(x-2)...(x-100)(x>100),求F'(X)](/uploads/image/z/3993703-7-3.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D%28x-1%29%28x-2%29...%28x-100%29%28x%3E100%29%2C%E6%B1%82F%27%28X%29)
设函数f(x)=(x-1)(x-2)...(x-100)(x>100),求F'(X)
设函数f(x)=(x-1)(x-2)...(x-100)(x>100),求F'(X)
设函数f(x)=(x-1)(x-2)...(x-100)(x>100),求F'(X)
lnf(x)=ln(x-1)+ln(x-2).+ln(x-100)
两侧求导得:f'(x)/f(x)=1/(x-1)+1/(x-2)+...+1/(x-100)
f'(x)=(x-1)(x-2)...(x-100)[1/(x-1)+1/(x-2)+...+1/(x-100)]
f'(X)=(x-1)(x-2)...(x-100)[1/(x-1)+1/(x-2)+...+1/(x-100)]=f(x)[1/(x-1)+1/(x-2)+...+1/(x-100)]
他应该不会要你求f(x)的导数的表达式,应该是求一个具体的数,也就是说最后一个括号里的x是一个常数。如果是这样,不要用公式,尝试一下求导的定义式,应该会得到答案。