Question

Usando a definição de derivada, derive a função F(x)=x²+10

Answer 1

$f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \\ \\ f'(x)= \lim_{h \to 0} \frac{(x+h)^2+10-(x^2+10)}{h}\\ \\ f'(x)= \lim_{h \to 0} \frac{x^2+2hx+h^2+10-x^2-10}{h}\\ \\ f'(x)= \lim_{h \to 0}\frac{2hx+h^2}{h}\\ \\ f'(x)= \lim_{h \to 0} \frac{h(2x+h)}{h}\\ \\ f'(x)= \lim_{h \to 0}(2x+h) = 2x+0=2x$