y=x^(x^2)求导
问题描述：
y=x^(x^2)求导
答
y=x^(x²)
lny=x²lnx
(1/y)y'=2xlnx+x²(1/x)
y'/y=2xlnx+x
y'=(2xlnx+x)x^(x²)
答
y=f(u)=x^u
u=g(x)=x^2
y=f[g(x)]
dy/dx=f'(u)*g'(x)
=ux^(u-1)*2x
=x^2*x^(x^2-1)*2x
=2x^(x^2+2)
答
(2xlnx+x)e^lnx(x^2)
答
dy/dx=x^(x^2)*lnx*2x
有点问题 重新来遍
y=e^(x^2*lnx)
dy/dx=e^(x^2*lnx)*(2xlnx+x^2*1/x)
=x^(x^2)*(2xlnx+x)
答
两边取对数
lny=x^2*ln|x|
两边求导
y'/y=2xln|x|+x^2/x
y'=y(2xln|x|+x)=x^(x^2)(2xln|x|+x)