Calcula utilizando la definición de derivada

Albert!

$$\begin{align}&f'(2)=\lim_{h \to 0} \frac{f(2+h)-f(2)}{h}=\\&\\&\\&\lim_{h \to 0} \frac{2(2+h)^2+5(2+h)-(8+10)}{h}=\\&\\&\lim_{h \to 0} \frac{2(4+4h+h^2)+10+5h-18}{h}=\\&\\&\lim_{h \to 0} \frac{8+8h+2h^2+10+5h-18}{h}=\\&\\&\lim_{h \to 0} \frac{2h^2+13h}{h}= \frac{0}{0}=\\&\\&\lim_{h \to 0} \frac{h(2h+13)}{h}=\\&\\&\lim_{h \to 0}(2h+13)=\\&\\&=13\end{align}$$

Saludos

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