y = xtanx
= xsinx/cosx
根据导数除法则：d(u/v) = (vdu - udv)/v²,导数乘法则：d(uv) = vdu + udv
dy = [cosxd(xsinx) - xsinxd(cosx)]/cos²x,整体先来个除法则,然后d(xsinx)里是乘法则
dy = [cosx(sinxd(x) + xd(sinx)) - xsinx(- sinx)]/cos²x
dy = [cosx(sinx • 1 + xcosx) + xsin²x]/cos²x
dy = (sinxcosx + xcos²x + xsin²x)/cos²x
dy = [sinxcosx + x(cos²x + sin²x)]/cos²x
dy = (sinxcosx + x)/cos²x
dy = tanx + xsec²x
y' = tanx + xsec²x
dy原本是求微分的意思,我这里暂时当作求导了,用着好看嘛.
如果你会tanx的导数的话,直接用乘法则可以了,正割secx = 1/tanx
y = xtanx
dy = tanxd(x) + xd(tanx)
dy = tanx • 1 + x • sec²x
dy = tanx + xsec²x