Question

Find the derivative of m(x)=1/x+4 by using the difference quotient.

m ' (x) =________

**how do you start??
thanks!!

Answer 1

Use equation editor first.

Answer 2

Or use parentheses.

Answer 3

Do you know what the quotient rule?

Answer 4

\[m(x)=1\div x+4\]

Answer 5

is that better?

and knx^(n-1) ?

Answer 6

^that doesn't help lol :P i mean use the fraction thingy

Answer 7

ohh hahah lemme try to find it :P

Answer 8

1/(x+4) or (1/x)+4

Answer 9

\[\frac{ 1 }{ x+4 }\]

Answer 10

use parentheses

Answer 11

\[m(x)= 1/(x+4)\] is that better?

Answer 12

yes:)

Answer 13

wait how do you put the fraction thingy? :O

Answer 14

in the equation tool?

and what happens from here?

Answer 15

Press buttons and find out :D there's a a/b button

Answer 16

you want \(\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h}=\lim_{h\rightarrow0}\frac{\frac{1}{(x+h)+4}-\frac{1}{x+4}}{h}\)

Answer 17

can you simplify that?

Answer 18

\[m(x)=\frac{1}{ x+4 }\]

Answer 19

oh yay!

Answer 20

okay um would i be multiplying by 1/h ?

Answer 21

simplify the top first

Answer 22

then multiply by 1/h, then some h's will cancel, then let the remaining h's be 0, then you have the answer

Answer 23

ermm \[(\frac{ 1 }{ h } - 1) /\] ??

Answer 24

* / h ?

Answer 25

did i simplify the top correctly?

Answer 26

just use power rule with chain rule
\[m = \frac{1}{x+1} = (x+1)^{-1}\]
\[m' = -(1)(x+1)^{-2} = -\frac{1}{(x+1)^2}\]

Answer 27

okay, so if my equation is m(x) = (1) / (x+4) it becomes...

=(x+4)^-1

m ' (x) = -(1)(x+4)^-2 = - (1) / (x+4)^2 ??

Answer 28

yes

Answer 29

and that's the final answer? :o

Answer 30

yes

Answer 31

awesome! thank you!

Answer 32

however if for example there is an "x" on top
\[\frac{x}{x+4}\]
then you must use quotient rule

Answer 33

oh okay :)

Answer 34

thank you!!!

Answer 35

yw