Question

Find the derivative of f(x) = 8/x at x = -1.

Answer 1

Use the normal rules for powers to find the derivitive

Then put x=-1 into that expression

EXAMPLE

\[f(x) = 5x ^{-2} \]

so multiply by the current exponent and reduce the exponent by 1

so
\[f'(x) = -10x ^{-3}\]

at x=2 this is
f'(x) = -10/8

Answer 2

Hint
\[\frac{ 8 }{ x} = 8x ^{-1}\]

Answer 3

Find the derivative of \[8x ^{-1}\] and then substitute -1 for x.