h t COS T cos t Step 3 As previously noted the given function f t 6t sin nt is the product of two differentiable functions of the form f t g t h t where g t 6t and h t sin t We determi h t cos nt So the last thing we must do before applying the product rule is to find g t g t 6t g t We now apply the product rule g t h t g t h t h t g t 6t os nt sin t Therefore we have the following result f t