Find the derivative, r'(t), of the vector function.r(t)=t sin(8t), t2, t cos(7t)Step 1The derivative of a vector function is obtained by differentiating each of its components. Thus, ifr(t)=f(t), g(t), h(t),where f, g, and h are differentiable functions, thenr'(t)=f'(t), g'(t), h'(t).Forr(t)=t sin(8t), t2, t cos(7t),we havef(t)= t sin(8t),which is a product. Using the Product Rule and the Chain Rule, we havef'(t)=.