Differentiate 𝑓(𝑥)=4cos(𝑥).

Sure, here is the step by step solution:

Step 1: Identify the function The function given is f(x) = 4cos(x).

Step 2: Apply the chain rule The chain rule states that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function. In this case, the outer function is 4cos(u) and the inner function is x.

Step 3: Differentiate the outer function The derivative of cos(u) with respect to u is -sin(u). So, the derivative of 4cos(u) with respect to u is -4sin(u).

Step 4: Differentiate the inner function The derivative of x with respect to x is 1.

Step 5: Apply the chain rule According to the chain rule, the derivative of f(x) = 4cos(x) is the derivative of the outer function times the derivative of the inner function. So, the derivative of f(x) = 4cos(x) is -4sin(x) * 1 = -4sin(x).

So, the derivative of f(x) = 4cos(x) is -4sin(x).