Question

1. Use a definição de derivada via limite para calcular as derivadas f'(x), respeitando o valor de x.

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Answer 1

Resposta:

Explicação passo-a-passo:

f'(x) = $\lim_{h \to \00}\frac{f(x+h)-f(x)}{h}\\\\f'(x)= \lim_{h \to \00} \frac{(x+h)^2+x+h-x^2-x}{h}\\\\f'(x)= \lim_{h \to \00}\frac{x^2+2hx+h^2+x+h-x^2-x}{y}\\\\f'(x)= \lim_{h \to \00}\frac{2hx+h^2+h}{h}\\\\f'(x)= \lim_{h\to \00} a_n \frac{h(2x+h+1)}{h}\\\\f'(x)=2x+1\\\\f'(1)=2.1+1=3$