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 \( f^\prime(x)=anx^{n - 1}\). 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 \(x
eq0\)), we have \(f^\prime(x)=-4\times1=-4\).

Answer:

\(-4\)