Derivative of a sum of power functions, evaluated at a point

First rewrite $f(x) = 2x^{-4} + 3x^3 - 5x$ so every term is in the form $cx^n$. Applying the power rule term by term: $\frac{d}{dx}[2x^{-4}] = -8x^{-5}$, $\frac{d}{dx}[3x^3] = 9x^2$, and $\frac{d}{dx}[-5x] = -5$. By the sum/difference and constant multiple rules, $f'(x) = -8x^{-5} + 9x^2 - 5$.

Now substitute $x = -1$: $(-1)^{-5} = -1$, so $-8(-1) = 8$. Also $9(-1)^2 = 9$. Adding these together with the constant term: $f'(-1) = 8 + 9 - 5 = 12$.