I’ve tried and tried and tried but understanding of how to do this question evades me. I have an entire sheet just covered in eraser marks and dull pencil etchings from this wretched thing. The thing that annoys me the most is that I think it isn’t even one of the tougher questions. Ugh.
Can anyone please help me with this?
Use the definition of a derivative to find the derivative of f(x) = (2-x)/(2+x)
Thank you in advance!!
✅ Answers
? Best Answer
f(x + h) = (2 – (x + h)) / (2 + (x + h)) = (2 – x – h) / (2 + x + h)
f(x + h) – f(x) =>
(2 – x – h) / (2 + x + h) – (2 – x) / (2 + x) =>
((2 – x – h) * (2 + x) – (2 – x) * (2 + x + h)) / ((2 + x + h) * (2 + x)) =>
(4 + 2x – 2x – x^2 – 2h – xh – (4 + 2x + 2h – 2x – x^2 – xh)) / ((2 + x + h) * (2 + x)) =>
(4 – x^2 – 2h – xh – 4 – 2h + x^2 + xh) / ((2 + x + h) * (2 + x)) =>
(-4h) / ((2 + x + h) * (2 + x))
Divide by h
-4 / ((2 + x + h) * (2 + x))
h goes to 0
-4 / ((2 + x) * (2 + x)) =>
-4 / (2 + x)^2
– Chosen by Asker