Question

用定义法求下列函数的导数。（1）y=x^2 （2）y=4/x^2

Answer 1

y=x�0�5
y'=lim [(x+h)�0�5-x�0�5]/h
=lim (x�0�5+2xh+h�0�5-x�0�5)/h
=lim (2xh+h�0�5)/h
=lim (2x+h)
=2x+0
=2x

y=4/x�0�5=4(1/x�0�5)
y'=4*lim [1/(x+h)�0�5-1/x�0�5]/h
=4*lim {[x�0�5-(x+h)�0�5]/[x�0�5(x+h)�0�5]}/h
=4*lim {-2xh-h�0�5/[x�0�5(x+h)�0�5]}*(1/h)
=4*lim (-2x-h)/[x�0�5(x+h)�0�5]
=4*(-2x)/[x�0�5(x�0�5)]
=-8/x�0�6

Answer 2

y=2x.y=-8/x的-3次方