(Solved): Question 1 Define the two vector valued functions of one variable \[ \boldsymbol{u}(t):=\left(-1 / ...

Question 1 Define the two vector valued functions of one variable \[ \boldsymbol{u}(t):=\left(-1 / t, 2 t, t^{2}\right), \quad \boldsymbol{v}(t):=\left(t^{2}, t,-t^{3}\right) . \] A. Use the formula for the derivative of a dot product to calculate \( (u \cdot v)^{\prime}(1) \). B. Calculate \( \boldsymbol{u} \cdot \boldsymbol{v} \) and using that calculate again the derivative \( (\boldsymbol{u} \cdot \boldsymbol{v})^{\prime}(1) \).