Question

求下列函数在指定点的导数1、f(x)=5x^3-2x^2+x-3,x0=02、f(x)=x/sinx,x0=π/23、y

Answer 1

1.f'(x)=15x^2-4x+1

f'(0)=1

2.f'(x)=(sinx-xcosx)/[(sinx)^2]

f'(π/2)=1

3.表意不明：

若f(x)=[x(8-x)]^(1/3)

则 f'(x)=(1/3){[x(8-x)]^(-2/3)}(8-2x)

f'(0)=0

若f(x)=x[(8-x)^(1/3)]

f'(x)=(8-x)^(1/3)-(x/3)[(8-x)^(-2/3)]

f'(0)=2