y=log[g(x)]f(x)的导数怎么解

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y=log[g(x)]f(x)的导数怎么解

y=log[g(x)]f(x)的导数怎么解
y=log[g(x)]f(x)的导数怎么解

y=log[g(x)]f(x)的导数怎么解
log[g(x)]f(x)= (ln f) / (ln g)
y' = [(ln f)/(ln g)]'= {[(ln g)'·ln f]-[(ln f)'·ln g]}/(ln g)^2
={ [ (ln f) / g ] - [ (ln g) / f ] } / (ln g)^2
= (f·ln f - g·ln g) / [ g·f·(ln g)^2 ]

g(x)是底数吗、

复合求导与乘积求导结合使用

y'={lg[g(x)]}'f(x)+lg[g(x)]f'(x)
=1/g(x) lge g'(x)f(x))+lg[g(x)]f'(x)