Final answer:
The derivative of the trigonometric function f(t) = cos(t) * t can be found using the product rule of differentiation.
Step-by-step explanation:
The derivative of the trigonometric function f(t) = cos(t) * t can be found using the product rule of differentiation. The product rule states that if two functions, u(x) and v(x), are multiplied together, the derivative of their product is given by (u'(x) * v(x)) + (u(x) * v'(x)).
Applying this rule to the function f(t) = cos(t) * t, we have u(t) = cos(t) and v(t) = t. Taking the derivatives of these functions, we find u'(t) = -sin(t) and v'(t) = 1.
Substituting these values into the product rule formula, we get f'(t) = (-sin(t) * t) + (cos(t) * 1), which simplifies to f'(t) = -t*sin(t) + cos(t).