Questão 6 Calcule a derivada segunda de \vec{r}(t)=\left(\fr...

Questão 6 Calcule a derivada segunda de \vec{r}(t)=\left(\frac{3}{t},\sen(t+t^{2}),e^{t}\right) e assinale a alternativa que a representa.

a) \vec{r}^{\prime\prime}(t)=\left(6t^{-3},(1+2t)\cos(t+t^{2}),e^{t}\right)

b) \vec{r}^{\prime\prime}(t)=\left(6t^{-3},(2\cos(t+t^{2})-\sen(t^{2}+t))-4(t+t^{2})\sen(t^{2}+t),e^{t}\right)

c) \vec{r}^{\prime\prime}(t)=\left(-3t^{-2},(1+2t)\cos(t+t^{2}),e^{t}\right)

d) \vec{r}^{\prime\prime}(t)=\left(6t^{-2},(2\cos(t+t^{2})-\sen(t^{2}+t))-4(t+t^{2})\sen(t^{2}+t),0\right)

e) \vec{r}^{\prime\prime}(t)=\left(-3t^{-2},(2\cos(t+t^{2})-\sen(t^{2}+t))-4(t+t^{2})\sen(t^{2}+t),e^{t}\right)

$Questão 6 Calcule a derivada segunda de \vec{r}(t)=\left(\frac{3}{t},\sen(t+t^{2}),e^{t}\right) e assinale a alternativa que a representa. a) \vec{r}^{\prime\prime}(t)=\left(6t^{-3},(1+2t)\cos(t+t^{2}),e^{t}\right) b) \vec{r}^{\prime\prime}(t)=\left(6t^{-3},(2\cos(t+t^{2})-\sen(t^{2}+t))-4(t+t^{2})\sen(t^{2}+t),e^{t}\right) c) \vec{r}^{\prime\prime}(t)=\left(-3t^{-2},(1+2t)\cos(t+t^{2}),e^{t}\right) d) \vec{r}^{\prime\prime}(t)=\left(6t^{-2},(2\cos(t+t^{2})-\sen(t^{2}+t))-4(t+t^{2})\sen(t^{2}+t),0\right) e) \vec{r}^{\prime\prime}(t)=\left(-3t^{-2},(2\cos(t+t^{2})-\sen(t^{2}+t))-4(t+t^{2})\sen(t^{2}+t),e^{t}\right)$

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