y=sinx的tanx次方求导

y = (sinx)^(tanx)
lny = tanx * ln(sinx)
y'/y = ln(sinx) * sec²x + tanx * 1/sinx * cosx
y'/y = ln(sinx) * sec²x + 1
y' = [1 + sec²xln(sinx)] * y
y' = [1 + sec²xln(sinx)] * (sinx)^(tanx)