Chain rule with graphs

Sep 2019
7
0
Arizona
I suppose the graph only stretches as far as x = 80 and y = 80, which makes finding the derivative at x = 5 a strange task. I tried doing proportions and slopes, but I knew I was working too hard. I am looking for help with the below problem.
screenshot.png
 
Dec 2014
131
102
USA


$\dfrac{d}{dx} f [g(x) ] = f'[g(x)] \cdot g'(x)$


$\dfrac{d}{dx} f \bigg[g(x) \bigg]_{x=5} = f'[g(5)] \cdot g'(5) = f'(42.5) \cdot g'(5)$

what is the slope of $f$ at $x=42.5$ ?

what is the slope of $g$ at $x=5$ ?
 
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