Question

Find the derivative f(x) = -7/x at x = -3

Answer 1

do you know the general formula ?

derivative of x^n is ?

Answer 2

isn't it the slope formula?

Answer 3

nah,
if \(f(x) = x^n \\ \large f'(x) = n x^{n-1}\)

heard of it ?

Answer 4

no. Do I just plug in x?

Answer 5

-7/x
since -7 is constant, it can be thrown out of the derivative
\((-7/x)' = (-7) (1/x)' = -7 (x^{-1})'\)

and for derivative of x^(-1)
you can use that general formula
just plug in n = -1

Answer 6

-7/-1?

Answer 7

no....plug in n = -1 in
n x^(n-1)

Answer 8

(-1) (-3)^(-1-1)
I don't get it.

Answer 9

got this ?