Differentiate sin 3x

To differentiate the function sin(3x), we need to apply the chain rule from calculus. The chain rule states that if you have a composite function, such as f(g(x)), then the derivative is:

f'(g(x)) * g'(x).

For our function:

• Let f(u) = sin(u) where u = 3x.
• The derivative of f(u) with respect to u is f'(u) = cos(u).
• Now, we need to find g'(x), the derivative of g(x) = 3x, which is simply g'(x) = 3.