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Problem 59 Hard Difficulty

The Michaelis-Menten equation for the enzyme chymotrypsin is

$ v = \frac {0.14[S]}{0.015 + [S]} $

where $ v $ is the rate of an enzymatic reaction and [S] is the concentration of a substrate S. Calculate $ dv/d[S] $ and interpret it.

Answer

$v^{\prime}(S)=\frac{0.0021}{(0.015+[S])^{2}}$

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Video Transcript

I mean, it's clear. So when you raid here, so let me, huh of us be equal to 0.1 for us. G f s vehicle thio 0.15 plus us. We'll be equal f over g and using the crow shit rule he over d us of f of us over Ji of us which is equal to G of us de over de us. Uh, of s minus off of us de over de s Jew of us all over two of s square. This becomes equal to 0.15 plus us, do you over deep US 0.1 for us, minus 0.1 for us. Be over D s 0.15 plus ness well over 0.15 plus square in this equals 0.21 over 0.15 Close s square. This represents the instantaneous acceleration of the reaction of the enzyme and it's in respect to the substrate s