高数 用定义求导

lim [x²f(x.)-x².f(x)]/(x - x.)
x→x.
= lim {[x²f(x.)-x²f(x)]+[x²f(x)-x².f(x)]}/(x - x.)
x→x.
= lim [x²f(x.)-x²f(x)]/(x - x.)
x→x.
+lim [x²f(x)-x².f(x)]/(x - x.)
x→x.
= lim x²[f(x.)-f(x)]/(x - x.)
x→x.
+lim [x²-x².]f(x)/(x - x.)
x→x.
= lim -x²[f(x) - f(x.)]/(x - x.)
x→x.
+lim [(x - x.)(x + x.)f(x)/(x - x.)
x→x.
= -x².f'(x.)+ 2x.f(x.)
= x.[2f(x.) - x.f'(x.)]