Question

using the derivative rule find the rate of change
8x^-7 - 6x^-2 - x^-5

Answer 1

\(f(x) = 8x^{-7} - 6x^{-2} - x^{-5}\)
Rate of change of f(x) is f'(x).
Just differentiate f(x) with respect to x.

Answer 2

\[\large
\frac{d}{dx}x^n = nx^{n-1} \\
\text{For example} \\
\frac{d}{dx}x^{-7} = (-7)x^{-7-1} = -7x^{-8} \\
\]