$\displaystyle f(x+h)-f(x)/h$
1)$\displaystyle f(x)=5x^3$
$\displaystyle f(x+h) = 5(x+h)^3 = 5(x^3+3x^2h+3xh^2+h^3)$
$\displaystyle f(x) = 5x^3$
Compute
$\displaystyle f(x+h) - f(x) = 5x^3 + 15x^2h+15xh^2+5h^3 - 5x^3 = 15x^2h+15xh^2+5h^3$
Don't forget to use the limit notation in your definition:
$\displaystyle \lim_{h\to 0} \frac{f(x+h)-f(x)}{h}=\lim_{h\to 0} \frac{15x^2h+15xh^2+5h^3}{h}=\lim_{h\to 0}15x^2+15xh+5h^2=...$
Good luck!