If y = cos 3x, find \( \frac{\delta y}{\delta x} \)

To find the derivative of y = cos 3x, we need to use the chain rule of differentiation. The chain rule states that if y = f(g(x)), then the derivative of y with respect to x is given by the product of the derivative of f with respect to g multiplied by the derivative of g with respect to x. In other words, δy/δx = δf/δg * δg/δx. Using the chain rule, we have: δy/δx = δ(cos 3x)/δ(3x) * δ(3x)/δx The derivative of cos 3x with respect to 3x can be found using the chain rule again: δ(cos 3x)/δ(3x) = -sin(3x) The derivative of 3x with respect to x is simply 3. Substituting these values in the original equation, we get: δy/δx = -sin(3x) * 3 Simplifying, we have: δy/δx = -3 sin(3x) Therefore, the correct option is -3 sin 3x. In summary, the derivative of y = cos 3x is -3 sin 3x, which is obtained using the chain rule of differentiation.