Evaluate $\frac{d}{dt}{\int }_{\tan t}^3\frac{dx}{x^5+3}$.

$-\frac{1}{{\tan }^{5}t+3}$

$\frac{{\sec }^{2}t}{{\tan }^{5}t+3}$

$-\frac{{\sec }^{2}t}{{\tan }^{5}t+3}$

$\frac{1}{{\tan }^{5}t+3}$