Question

Calcule a derivada pela definição de f(x)=x^2+x

Answer 1

f(x)=x^2+x

f'(x)=2x + 1 ✓

Answer 2

Resposta:

Explicação passo-a-passo:

$f'(x)= \lim_{h \to 0}\dfrac{f(x+h)-f(x)}{h} \\\\\\f'(x)= \lim_{h \to 0}\dfrac{(x+h)^{2}+x+h -(x^{2}+x)}{h}\\\\f'(x)= \lim_{h \to 0}\dfrac{x^{2}+2hx+h^{2}+x+h-x^{2}-x}{h}\\\\f'(x)= \lim_{h \to 0}\dfrac{2hx+h^{2}+h}{h}\\\\f'(x)= \lim_{h \to 0}\dfrac{(2x+h+1)h}{h}\\\\f'(x)= \lim_{h \to 0}(2x+h+1)\\\\f'(x)= 2x+0+1\\\\f'(x)=2x+1$