Question

Find the derivative of x/x+1 by using the 4-step rule (definition).

Answer 1

are you using the quotient rule?

Answer 2

yes.

Answer 3

it says "definition" which i would take to mean
\[\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}\]
i saw this exact question 2 days ago
raft of algebra

Answer 4

Sounds to me as though using the quotient rule here would be unacceptable (except to check your work), since the directions specify use of the "4-step rule" (definition of the derivative).

Answer 5

If f(x)=x / (x+1), what is f(x+h)?

Write out f(x+h)-f(x).

Your result will involve fractions. Identify the LCD and combine those two fractions into one.

More instructions after you've done this.

Answer 6

Find the derivative of f(x) = x/x+1:

1) To find / evaluate f(x+h), replace each appearance of x here with (x+h).

Answer 7

@conan.195114: New to OpenStudy? If so, welcome.
I checked your status and learned that you're supposedly "offline." Next time others try to help you, PLEASE acknowledge their efforts and tell them of your intent to leave the conversation.

Answer 8

sorry.. i need to take a break.. and yeah your step 1 is correct and im currently stuck at step 2 if you know what i mean.. and thanks for all your efforts i really appreciate it

Answer 9

\[\large \lim_{h \rightarrow 0} \frac{\frac{x+h}{x+h+1} - \frac{x}{x+1}}{h}\]
combine fractions on top
\[\rightarrow \frac{(x+h)(x+1) - x(x+h+1)}{(x+h+1)(x+1)} = \frac{h}{(x+h+1)(x+1)}\]
now the h's will cancel leaving
\[\lim_{h \rightarrow 0} \frac{1}{(x+h+1)(x+1)} = \frac{1}{(x+1)^2}\]

Answer 10

Conan:

Step 1: I asked you to evaluate f(x) = x / (x+1) at x+h by replacing every occurrence of x with (x+h) (preferably inside parentheses).

Step 2: subtract the original f(x) from your f(x+h):\[\frac{ x+h }{ x+h+1 }-\frac{ x }{ x+1 }\]

Step 3: combine these fractions into one by identifying and using the LCD. See the work done by "dumbcow," above.

Step 4: remembering that the definition of the derivative is\[\frac{ dy }{ dx }= (\lim~as~h \rightarrow 0)~of~\frac{ f(x+h)-f(x) }{ h },\]
divide your previous result (Step 3) by h, and then cancel the two letters 'h'

Step 5: Take the limit of the result as h goes to zero.

Step 6: Label your result: f '(x) = 1 / (x+1)^2

I'd suggest y ou study this, then try finding the derivative again on your own.