Question

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 \( f^\prime(x)=nax^{n - 1} \). For \( f(x)=-4x=-4x^1 \), here \( a=-4 \) and \( n = 1 \).

Step2: Calculate the derivative

Using the power rule: \( f^\prime(x)=1\times(-4)x^{1-1}=-4x^0 \). Since \( x^0 = 1\) (for \( x
eq0\), and in the context of derivatives of polynomial - like functions, we consider the general form), so \( f^\prime(x)=-4\).

Answer:

\( f^\prime(x)=-4 \) (the fourth option)