Question

Qual é a alternativa correta que apresenta a derivada da função g(x)...

Answer 1

$\displaystyle \underline{\text{Derivando uma fun{\c c}{\~a}o dada por uma integral}}\\\\\\ \text{g(x)}=\int\limits^{\text x}_1\sqrt{\text t^2-3\text t+5}\ \text{dt} = \text{G(x)}-\text {G(1) } \\\\ \underline{\text{onde}}: \\\\ \text {G {\'e} a primitiva de }\sqrt{\text t^2-3\text t+5}\ , \text{ou seja, \text G'(t) =}\sqrt{\text t^2-3\text t+5} \\\\ \underline{\text{Ent{\~a}o}}: \\\\\ \text{g'(x)} = \text{G'(x)} \\\\ {\text {obs}}: \text {G'(1)} = 0 \to \text{constante}$

Portanto :

$\huge\boxed{\ \text{g'(x)}=\sqrt{\text x^2-3\text x+5} \ }\checkmark$

letra b