To find the derivative of y = 3 sin(-4x) with respect to x, we will use the chain rule. The chain rule states that if you have a composite function f(g(x)), then the derivative is f'(g(x)) g'(x).

In this case, y = 3 sin(-4x), and we can treat 3 as a constant multiplier. Let's find the derivative step by step:

1. Differentiate the outer function (3) with respect to x (which is 0):

d(3)/dx = 0

2. Differentiate the inner function (-4x) with respect to x:

d(-4x)/dx = -4

3. Differentiate the sine function:

d(sin(u))/du = cos(u), where u is the argument of the sine function.

Now, applying the chain rule:

dy/dx = (d(3)/dx) sin(-4x) + 3 (d(sin(-4x))/dx)

Since d(3)/dx is 0, the first term disappears:

dy/dx = 0 + 3 (cos(-4x) (-4))

Now, simplify the expression:

dy/dx = -12 cos(-4x)