Question

Find the derivative of f(x) = 5/x at x = -1

Answer 1

using the limit definition of derivative?

Answer 2

or you want it the usual way?

Answer 3

factor out the 5 and find the derivative of 1/x as we did before

Answer 4

so it's 5(1/x), right?

Answer 5

correct. now we have \(\large 5\frac{d}{dx}\frac{1}{x}\)

Answer 6

I honestly can't remember this next part but I'm gonna take a wild guess and go with 5(1/x^2)...?

Answer 7

You shouldn't be guessing.

Why is that the case? What is the derivative of \(\frac{1}{x}\)?

Answer 8

oops
no guessing hehe

Answer 9

x^-1?

Answer 10

\(\large \frac{1}{x}=x^{-1}\)

Answer 11

okay, so we plug it into the power rule now?

Answer 12

correct.

Answer 13

f(x)=x^-1 -> -x^(-1-1) -> -x^-2

Answer 14

nice. yeah.

so now bring it back to the original equation.

\(\large 5\frac{d}{dx}\frac{1}{x}=5*\frac{1}{x^2}=\frac{5}{x^2}\)

Answer 15

and then plug in -1 for x
so it's 5/1 or just 5?

Answer 16

looks right

Answer 17

It's finally making sense! Thanks :D

Answer 18

yay, I'm so proud ;~;