What is the Limit Definition of a Tough Derivative?

[member 428835]

hey pf!

can you help me with this $$\lim_{h \to 0} \frac{f(x+3h^2) - f(x-h^2)}{2h^2}$$

i know the definition and have tried several substitutions, but no help. anyone have any ideas?

 

[member 428835]

nevermind, lopitals rule did the trick

 

[lurflurf]

hint 1
$$0=\mathrm{f}(x)-\mathrm{f}(x)$$
hint 2

Spoiler

$$\lim_{h \to 0} \frac{f(x+3h^2) - f(x-h^2)}{2h^2}=\lim_{h \to 0}\left[\frac{3}{2}\frac{\mathrm{f}(x+3h^2)-\mathrm{f}(x)}{3h^2}+\frac{1}{2}\frac{\mathrm{f}(x-h^2)-\mathrm{f}(x)}{-h^2}\right]$$