Differentialquotient:
$$f'(x_0)=\lim_{h \to 0}\frac{f(x_0+h)-f(x_0)}{h}$$
Werte richtig einsetzen: \(f(x)=4x^2\)
$$f'(5)=\lim_{h \to 0} \frac{f(5+h)-f(5)}{h} =\lim_{h \to 0} \frac{4(5+h)^2-4\cdot5^2}{h}\\=\lim_{h \to 0}\frac{100+40h+4h^2-100}{h} =\lim_{h \to 0}\frac{40h+4h^2}{h}=\lim_{h \to 0}40+4h=40$$