Question

定义法证明f(x)*g(x)导数

Answer 1

d[f(x)g(x)]/dx = lim[f(x+dx)g(x+dx) - f(x)g(x)/dx = lim [f(x+dx)g(x+dx)-f(x+dx)g(x) + f(x+dx)g(x) - f(x)g(x)]/dx

= lim {f(x+dx)[g(x+dx) -g(x)}/dx + lim {g(x)[f(x+dx)-f(x)]/dx}

= f(x)g'(x)+f'(x)g(x)