Question

x^(xlnx)求导?对数恒等式是什么?顺便告诉我几个有关对数的运算公式?

Answer 1

y=x^(xlnx)

ln y = x (ln x) (ln x)=x (ln x)^2

y'/y = (ln x)^2 + 2x (ln x)/x = (ln x)^2 + 2 ln x = ln x (ln x + 2)

y' = x^(xlnx) lnx (lnx+2)

几个公式：

1,换底公式：log a X = log b X / log b a

2,log a X = Y,X = a^Y

3,log XY = log X + log Y

4,Y = ln X Y'=1/X X = e^Y

5,等等