Question

find the equation of the tangent line y= √x/(x+1) (4,0.4)

Answer 1

find the derivative
replace \(x\) by 4 to get the slope
use the point slope formula to find the equation for the line
do you have the derivative?

Answer 2

I keep getting confused when getting the derivative.

Answer 3

quotient rule for this one

\[(\frac{f}{g})'=\frac{gf'-fg'}{g^2}\]

Answer 4

no need to do much algebra to simplify, just make sure it is in the form where you can replace \(x\) by 4

Answer 5

get
\[\frac{(1+x)\frac{1}{2\sqrt{x}}-\sqrt{x}}{(x+1)^2}\] by direct substitution in to quotient rule

Answer 6

i got -1/50, not sure if it's right

Answer 7

let me see what i get

Answer 8

i think i get something diffrerent

Answer 9

i get

\[\frac{\frac{5}{4}-2}{25}=-\frac{3}{100}\]

Answer 10

check my arithmetic, but i think it is right

Answer 11

yeah i got that the second time, but when i search it up on different websites ppl got like 1/50