Final answer:
To differentiate the given function y = c cos(t) t² sin(t), we can use the product rule. The derivative of y with respect to t is -ct² sin(t) + c(2t sin(t) + t² cos(t)).
Step-by-step explanation:
To differentiate the given function, y = c cos(t) t² sin(t), we can use the product rule of differentiation. Let's break down the function into two parts: f(t) = c cos(t) and g(t) = t² sin(t). Then, we can apply the product rule:
f'(t) = -c sin(t) and g'(t) = 2t sin(t) + t² cos(t).
Finally, we can combine the derivatives using the product rule: y'(t) = f'(t)g(t) + f(t)g'(t) = -ct² sin(t) + c(2t sin(t) + t² cos(t)).