Question

Find the derivative of f(x) = 5 divided by x at x = -1.

Answer 1

use the power rule, keep in mind that \(\bf f(x)=\cfrac{5}{x}\implies f(x)=5x^{-1}\)

Answer 2

okay can u show me how to go from there, 5x^-1 is probably easier to use in the power rule formula right?

Answer 3

yes... the other way would be using the product formula, which will be a bit longer, is all

Answer 4

rather the "quotient" formula

Answer 5

\(\bf f(x)=\cfrac{5}{x}\implies f(x)=5x^{{\color{red}{ -1}}}\implies f(x)={\color{red}{ -1}}\cdot 5\cdot x^{{\color{red}{ -1}}-1}\)

Answer 6

that'd give you the derivative equation, then just plug in "-1" for its "x" argument

Answer 7

okay so would the derivative be -5?

Answer 8

no

Answer 9

what is -1-1

Answer 10

-2

Answer 11

that is your exponent on x

Answer 12

okay so x^-2 or 1/x^2 right?

Answer 13

\(\bf f(x)=\cfrac{5}{x}\implies f(x)=5x^{{\color{red}{ -1}}}\implies f(x)={\color{red}{ -1}}\cdot 5\cdot x^{{\color{red}{ -1}}-1}
\\ \quad \\
f'(x)=-5x^{-2}\qquad \textit{when x = -1, thus}\quad f'({\color{blue}{ -1}})=-5({\color{blue}{ -1}})^{-2}\)

Answer 14

ohhhhhh okayy so i would simplify then plug in the x=-1 in for x in the new equation

Answer 15

yeap

Answer 16

okay so the derivative is -5 right?

Answer 17

yeap

Answer 18

the derivative isnt -5. but at f(-1)=-5

Answer 19

f'(-1)

Answer 20

right

Answer 21

ohhhhhh okayyyy thank youuu so muchhh, really helpfull

Answer 22

yw