Answer
$r'(t)=3t^{2}i-3j$
Work Step by Step
To find the derivative of a vector-valued function, you take the derivative of each individual component. Therefore, one can take the derivative using power rule of derivatives ($(x^{n})'=nx^{n-1}$).
$r'(t)=(t^{3})'i-(3t)'j$
$r'(t)=(3t^{3-1}i-3j=3t^{2}i-3j$
