CamTutor

Question - Finding the Derivative of a Function Involving a Product of a Polynomial and a Trigonometric Function

Для нахождения производной данной функции \( f(x) = (4x^4 + 2) \cos(x) \), воспользуемся правилом произведения.

\( f'(x) = (4x^4 + 2)' \cos(x) + (4x^4 + 2) \cdot (\cos(x))' \)

\( f'(x) = (16x^3) \cos(x) + (4x^4 + 2) \cdot (-\sin(x)) \)

\( f'(x) = 16x^3 \cos(x) - (4x^4 + 2) \sin(x) \)

Итак, производная функции \( f(x) \):

\( f'(x) = 16x^3 \cos(x) - (4x^4 + 2) \sin(x) \)

CamTutor

In regards to math, we are professionals.