Question

y=sinx的tanx次方求导如题

Answer 1

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)