Derivative of a negative power function evaluated at a point

Using the power rule, $f'(x) = -4x^{-4-1} = -4x^{-5}$. This follows directly from $\frac{d}{dx}[x^n] = nx^{n-1}$ with $n=-4$.

Now substitute $x=2$: $f'(2) = -4(2)^{-5} = -4\cdot\frac{1}{32} = -\frac{1}{8}$.

The derivative is negative four times x to the negative fifth power, so the coefficient is negative four. This comes directly from multiplying the original exponent, negative four, out front using the power rule. The negative sign here is what ultimately makes the final answer negative once we substitute x equals two.