Question

Find the derivative of f(x) = 4 divided by x at x = 2.

Answer 1

use
\[\frac{ d }{ dx }[x^n]=nx^{n-1}\]

Answer 2

I haven't learned that yet (Pre-calc) We use the Difference Quotient

Answer 3

all right
so take \[f(x)=4/x\]
so \[f(x+h)=4/(x+h)\]
ok?

Answer 4

ok

Answer 5

\[f'(x)=\lim_{h \rightarrow 0}\frac{ f(x+h)-f(x) }{ h}\]
familiar with this?

Answer 6

yes, we subtract 4/x, divide all by h

Answer 7

ok now just put values of f(x) and f(x+h) inside the limit
\[f'(x)=\lim_{h \rightarrow 0}\frac{ 4 }{ h }[\frac{ 1 }{ (x+h) }-\frac{ 1 }{ x }]\]
ok??

Answer 8

ok

Answer 9

now just simplify it
\[f'(x)=\lim_{h \rightarrow 0}\frac{ 4 }{ h }[\frac{ x-x-h }{ (x+h)x}]\]
\[f'(x)=\lim_{h \rightarrow 0}[\frac{ -4 }{ x(x+h)}]=\frac{ -4 }{ x^2}\]

Answer 10

got this?

Answer 11

yes

Answer 12

now just put x=2
so it will be\[f'(2)=\frac{ -4 }{ 2^2}=-1\]

Answer 13

Got it

Answer 14

Thanks

Answer 15

np :)