Calcular la derivada por definición:
$f(x)=7x-1$
Solución
| Definición de derivada | ||
| $f'(x)=\lim \limits_{h \to 0}{\dfrac{f(x+h)-f(x)}{h}}$ | ||
| Calculando $f(x+h)$ | ||
| $f(x+h)=7(x+h)-1$ | ||
| $f(x+h)=7x+7h-1$ | ||
| Reemplazando: | ||
| $f'(x)=\lim \limits_{h \to 0}{\dfrac{f(x+h)-f(x)}{h}}$ | ||
| $f'(x)=\lim \limits_{h \to 0}{\dfrac{7x+7h-1-(7x-1)}{h}}$ | ||
| $f'(x)=\lim \limits_{h \to 0}{\dfrac{7x+7h-1-7x+1}{h}}$ | ||
| $f'(x)=\lim \limits_{h \to 0}{\dfrac{7h}{h}}$ | ||
| $f'(x)=\lim \limits_{h \to 0}{7}$ | ||
| $f'(x)=7$ | ||
| Respuesta: | ||
| $f'(x)=7$ | ||