(1) 当x≠0时,
f'(x)=(2xsinxcosx-sin²x)/x²,
于是
f'(π/2)=[πsin(π/2)cos(π/2)-sin²(π/2)]/(π/2)²=-4/π²
(2)f'(0)=lim(x→0)[f(x)-f(0)]/x=lim(x→0)[(sin²x)/x]/x=lin(x→0)[(sinx)/x]²=1
(1) 当x≠0时,
f'(x)=(2xsinxcosx-sin²x)/x²,
于是
f'(π/2)=[πsin(π/2)cos(π/2)-sin²(π/2)]/(π/2)²=-4/π²
(2)f'(0)=lim(x→0)[f(x)-f(0)]/x=lim(x→0)[(sin²x)/x]/x=lin(x→0)[(sinx)/x]²=1