If y = 3 cos 4x, dydx d y d x equals

If y = 3 cos 4x, $\frac{dy}{dx}$ equals

Answer Details

To differentiate y = 3 cos 4x, we will use the chain rule of differentiation. The chain rule states that if y = f(g(x)), then y' = f'(g(x))g'(x). Here, f(x) = 3 cos x, and g(x) = 4x. So, f'(x) = -3 sin x, and g'(x) = 4. Using the chain rule, we have: y' = f'(g(x))g'(x) = -3 sin (4x) * 4 = -12 sin (4x) Therefore, the derivative of y = 3 cos 4x is y' = -12 sin (4x).