| lim |
| x→0 |
| f(x0+x)−f(x0) |
| x |
∴
| lim |
| x→0 |
| f(x0+x)−f(x0−3x) |
| x |
| lim |
| x→0 |
| f(x0+x)−f(x0)+f(x0)−f(x0−3) |
| x |
=
| lim |
| x→0 |
| f(x0+x)−f(x0) |
| x |
| lim |
| x→0 |
| f(x0−3x)−f(x0) |
| −x |
=f′（x0）+3
| lim |
| x→0 |
| f(x0−3x)−f(x0) |
| −3x |
=f′（x0）+3f′（x0）=4f′（x0），
故选D．
| lim |
| x→0 |
| f(x0+x)−f(x0−3x) |
| x |
| lim |
| x→0 |
| f(x0+x)−f(x0) |
| x |
| lim |
| x→0 |
| f(x0+x)−f(x0−3x) |
| x |
| lim |
| x→0 |
| f(x0+x)−f(x0)+f(x0)−f(x0−3) |
| x |
| lim |
| x→0 |
| f(x0+x)−f(x0) |
| x |
| lim |
| x→0 |
| f(x0−3x)−f(x0) |
| −x |
| lim |
| x→0 |
| f(x0−3x)−f(x0) |
| −3x |