find the derivative of the given equation f(x) = -4x

Explanation:

Step1: Apply the power rule

The power rule states that if ( f(x) = ax^n ), then ( f^\prime(x)=anx^{n - 1}). For ( f(x)=-4x=-4x^1), (a=-4) and (n = 1).

Step2: Calculate the derivative

Using the power rule (f^\prime(x)=-4\times1\times x^{1 - 1}). Since (x^{0}=1) (for (x\neq0)), we have (f^\prime(x)=-4\times1=-4).

Answer:

(-4)