What is the derivative?

Question

Find the derivative of the following above equation^

The final result shouldn't have I, j, or k. It should only have the variable t

Answer 1

First, take the dot product of the two vectors which give just a scalar equation

y = 8t²cos(t) + √tsin(2t) + 20

dy/dt = 16tcos(t) -8t²sin(t) + sin(2t)/(2√t) +2√tsin(2t)