Answer:
-0.013
Step-by-step explanation:
You want the slope of the curve y = x/(x² -1) at x = 9.
Derivative
The derivative can be found using the chain rule:
(uv)' = u'v +uv'
Here, we have ...
u = x
v = (x² -1)^-1
Then ...
u' = 1
v' = -1(x² -1)^-2·(2x)
The sum is ...
y' = 1/(x² -1) -2x²/(x² -1)²
Slope
At the point where x = 9, this is ...
y' = 1/(9² -1) -2(9²)/(9² -1)² = 1/80 -162/80² = -82/6400 = -41/3200
y'(9) ≈ -0.013
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