Using Product rule, in which u and v are taken as one
d(uvw)dx=d(uv)dxw+d(w)dxuvw.v.d(u)dx+w.u.d(v)dx+u.v.d(w)dx
Now using logarithmic,
y=uvw
taking log on both sides, we have
logy=logu+logv+logw1ydydx=1ududx+1vdvdx+1wdwdx∴dydx=y×(1ududx+1vdvdx+1wdwdx)dydx=w.v.d(u)dx+w.u.d(v)dx+u.v.d(w)dx
since y=uvw