设函数f(x)存在二阶导数,y=f(lnx),则y''=A、(1/x^2)[f''(lnx)+f'(lnx)]B、(1/x^2)[f''(lnx)-f'(lnx)]C、(1/x^2)[xf''(lnx)-f'(lnx)]D、(1/x^2)[xf'(lnx)-f''(lnx)]
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 03:35:24
![设函数f(x)存在二阶导数,y=f(lnx),则y''=A、(1/x^2)[f''(lnx)+f'(lnx)]B、(1/x^2)[f''(lnx)-f'(lnx)]C、(1/x^2)[xf''(lnx)-f'(lnx)]D、(1/x^2)[xf'(lnx)-f''(lnx)]](/uploads/image/z/1698750-54-0.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E5%AD%98%E5%9C%A8%E4%BA%8C%E9%98%B6%E5%AF%BC%E6%95%B0%2Cy%3Df%28lnx%29%2C%E5%88%99y%27%27%3DA%E3%80%81%281%2Fx%5E2%29%5Bf%27%27%28lnx%29%2Bf%27%28lnx%29%5DB%E3%80%81%281%2Fx%5E2%29%5Bf%27%27%28lnx%29-f%27%28lnx%29%5DC%E3%80%81%281%2Fx%5E2%29%5Bxf%27%27%28lnx%29-f%27%28lnx%29%5DD%E3%80%81%281%2Fx%5E2%29%5Bxf%27%28lnx%29-f%27%27%28lnx%29%5D)
设函数f(x)存在二阶导数,y=f(lnx),则y''=A、(1/x^2)[f''(lnx)+f'(lnx)]B、(1/x^2)[f''(lnx)-f'(lnx)]C、(1/x^2)[xf''(lnx)-f'(lnx)]D、(1/x^2)[xf'(lnx)-f''(lnx)]
设函数f(x)存在二阶导数,y=f(lnx),则y''=
A、(1/x^2)[f''(lnx)+f'(lnx)]
B、(1/x^2)[f''(lnx)-f'(lnx)]
C、(1/x^2)[xf''(lnx)-f'(lnx)]
D、(1/x^2)[xf'(lnx)-f''(lnx)]
设函数f(x)存在二阶导数,y=f(lnx),则y''=A、(1/x^2)[f''(lnx)+f'(lnx)]B、(1/x^2)[f''(lnx)-f'(lnx)]C、(1/x^2)[xf''(lnx)-f'(lnx)]D、(1/x^2)[xf'(lnx)-f''(lnx)]
选B 利用复合函数求导法则很容易带出 y'=f'(lnx)*(lnx)'=1/x*f'(lnx)
f''=-(1/x²)*f'(lnx)+1/x*f''(lnx)*1/x
'=-(1/x²)*f'(lnx)+1/x²*f''(lnx)
=(1/x²)[f''(lnx)-f'(lnx)]
每次求复合导数时要将自变量的导数乘上,当自变量为x时其导数为1
y'=f'(lnx)*(lnx)'=1/x*f'(lnx)
f''=-(1/x²)*f'(lnx)+1/x*f''(lnx)*1/x
'=-(1/x²)*f'(lnx)+1/x²*f''(lnx)
=(1/x²)[f''(lnx)-f'(lnx)]
选B