Найти производную:

1) f (x) = x/x^2+1 при x=0

2) f (x) = x*sinx при x=0

1) f (x) = x / (x²+1)

f' (x) ' = (1. (x²+1) - x. 2x) / (x²+1) ² = (x²+1-2x²) / (x²+1) ² = (1-x²) / (x²+1) ²

f' (0) = (1-0²) / (0²+1) ²=1/1=1

2) f (x) = x. sinx

f' (x) = 1. sinx+x. cosx=sinx+xcosx

f' (0) = sin0+0. cos0=0+0.1=0+0=0

((u/v) ' = (u'v-uv') / v², (uv) '=u'v+uv')