Differentiate.
-cos 2t cos 3t
A) -sin 2t cos 3t - cos 2t sin 3t
B) 2sin 2t cos 3t + 3cos 2t sin 3t
C) -2sin 2t cos 3t - 3cos 2t sin 3t
D) none of these

Question

Quizplus · Accepted Answer

We can use the product-to-sum formula for cosine to write:

cos 2t cos 3t = (1/2)(cos(2t+3t) + cos(2t-3t))
cos 2t cos 3t = (1/2)(cos 5t + cos (-t))
cos 2t cos 3t = (1/2)(cos 5t + cos t)

Now taking the derivative:

d/dt (cos 2t cos 3t) 
= d/dt (1/2)(cos 5t + cos t) 
= -(1/2)sin 5t + (1/2)sin t 
= -2sin 2t cos 3t - 3cos 2t sin 3t

Therefore, the correct answer is (C).

Differentiate. -Cos 2t Cos 3t