Question

设y=(sin2x)^x，求dy/dx

设y=(sin2x)^x，求dy/dx
最好过程能具体点啦

Answer 1

这个题目有问题，必须加个条件才行，在不考虑定义域的情况下
lny=xlnsin2x
y'/y=lnsin2x+xxcos2x/sin2x
y'=(lnsin2x+xxcos2x/sin2x)*y=(lnsin2x+xxcos2x/sin2x)(sin2x)^x

Answer 2

y= (sin(2x))^x
lny = xln(sin(2x))
(1/y)y' = 2xcos(2x)/sin(2x) +ln(sin(2x))
y' =[2xcos(2x)/sin(2x) +ln(sin(2x))] (sin(2x))^x