Find the derivative of the function and simplify your answer by using the trigonometric identities

Question

Find the derivative of the function and simplify your answer by using the trigonometric identities ​  ​

Quizplus · Accepted Answer

The function can be written as:
f(x) = (3x^2 + 4x + 1) sin(x)

Using product rule:
f'(x) = (6x + 4) sin(x) + (3x^2 + 4x + 1) cos(x)

Applying trigonometric identities:
f'(x) = (6x + 4) sin(x) + (3x^2 + 4x + 1) cos(x)
f'(x) = (6x + 4) sin(x) + 3x^2 cos(x) + 4x cos(x) + cos(x)
f'(x) = (6x + 4) sin(x) + (3x^2 + 4x) cos(x) + cos(x) + cos(x)

Simplifying,
f'(x) = (6x + 4) sin(x) + (3x^2 + 4x) cos(x) + 2cos(x)

Therefore, the answer is choice C.

Find the Derivative of the Function and Simplify Your Answer