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The biomass $ B(t) $ of a fish population is the …

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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.


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Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

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Derivatives

Differentiation

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Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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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

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Calculus: Early Transcendentals

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Top Calculus 1 / AB Educators
Catherine Ross

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Kayleah Tsai

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Samuel Hannah

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Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
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02:52

'The Michaelis-Menten equation for the enzyme chymotrypsin is 0.14[S] 0.015 [S]…

01:39

The Michaelis-Menten equation for the enzyme chymotrypsin is $$v=\frac{0.14[\m…

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The Michaelis-Menten equation models the rate $v$ of an enzymatic reaction as a…

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Michaelis-Menten equation describes enzyme kinetics in the simplest fashion. Th…

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The rate equation for an enzyme subject to competitive inhibition is $$V_{0}=\f…

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According to the Michaelis-Menten equation (Figure 7), when an enzyme is combin…

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According to the Michaelis-Menten equation (Figure $7 ),$ when an enzyme is com…

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According to the Michaelis-Menten equation, when an enzyme is combined with a s…
Additional Mathematics Questions

02:29

6) Jim 80O In(1 + 7e

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