Answer
$r'(t)=6i-14tj+3t^{2}k$
Work Step by Step
To find the derivative of a vector-valued function, take the derivative of each component. Therefore,
$r'(t)=(6t)'i-(7t^{2})'j+(t^{3})'k$
Use the power rule for derivatives ($(x^{n})'=nx^{n-1}$) to differentiate each component.
$r'(t)=6i-(7(2)t^{2-1})j+3t^{3-1}k = 6i-14tj+3t^{2}k$
